Dear TRS: Live from Atlantic City

That's right folks, it's time for another exciting edition of Dear TRS, where your questions are answered and all your dreams come true!

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Dear TRS: Why did you take so long to put out another one of these?

Sincerely,

Terry Lean
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Dear Terry,

It's the kindness and concern which people like you have shown me throughout this difficult time which has enabled me to make it through. More specifically, I refer to the excellent content on other people's websites which has enabled me to put off updating mine.
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Dear TRS: What do you think of Lipa's new CD?

Sincerely,

St. Mary
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Dear R' Mary,

In general Lipa's albums have been following an interesting track. As you look through them you'll see that the production values have really gotten better as time goes by- by that I mean that the albums sound much more professional and well produced. At the same time, the music has gotten much "shtickier". I don't necessarily mean that Lipa's songs make for better ear-worms, but rather that instead of just music they're filled with all sorts of shtick. At the same time, his songs have gone from being Yom Tov Ehrlich-like, long, not too much music, plenty of Yiddish which I don't have half a hope of understanding, to a much more accessible style, much simpler, using a lot more Hebrew and more complicated melodies and whatnot. If I was a music insider (or even if I thought I was one [in point of fact, it's the same thing]) I'm sure I could express myself much better. If the late, great Chaim Rubin was still blogging, I'm sure he'd have lots to say on this. That's not to say that I don't like the new albums, I really do, but they're a very different style.
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Dear TRS: That answer was quite serious, quite eloquent, quite unlike you.

Sincerely,

The other guy next door
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Dear Karl,

Was that supposed to be nice?
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Dear TRS: What do you think of women sitting together with men during services in synagogue?

Sincerely,

Sara H.
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Dear Sara,

Why would women want to do that? Do they have any idea what goes on in the men's section of your typical Shul? Do you know the last time these people took showers? Hello?
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Dear TRS: I went on a date last night, and the girl looked great. Really, she must have spent upwards of thirty five hundred dollars on her wardrobe, and three hours (conservative estimate) on her hair (not to mention her nails). I told her that she looked really nice. Or something like that. She did not respond positively. I can't go into the details, but let's just say that she went Robin Williams on my Mercedes after the date. What did I do wrong?

Sincerely,

Considering suing for treble damages
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Dear In need of a lawyer,

You seem to be laboring under a delusion here, which has not only cost you significant amounts of money but has also let this great catch get away. The way of the woman is mysterious, but there are certain rules which should always be followed when dealing with this dangerous and elusive quarry. Here's a nine point checklist you should follow:

1. Wear the right camouflage or else the girl will spot you and run away.

2. Relax. Before trying to stalk a girl you must be relaxed. Most people get overexcited when they spot a girl so you must remember to stay calm.

3. Find a girl track. Girl tracks look like two parallel almond-shaped prints that are pointed on the top end. Follow the tracks in the direction of the pointed end.

4. After following the track for a while to see which direction it is going, check the map to see where the direction will take you. Try to avoid following the girl if there are any big rivers or heavy bush to walk through, because girl will run right through it when they are spooked and you will never be able to follow the track.

5. Once you know that there isn’t anything that will get in your way, start heading in the direction of the girl.

6. Look out for coyotes or wolves, because you’ll be hunting during girl mating season and they are vulnerable to coyote and wolf attacks. If the coyotes and wolves are hungry enough, there is a chance that they will attack men, so be careful.

7. Pay attention to the trees and the bushes because the girl may have stopped to eat or defecate; by looking at the feces and checking its temperature, you can tell how long ago the girl was there.

8. If you find a sign that can tell you that the girl was there within half an hour, you may be extremely close to the girl and may spook it.

9. Once you think you are close to the girl, stop and make a girl call for a minute or two. If you hear the girl call back, you know you are within viewing range. Set up and wait for the girl. Once it is close enough to you, try to make the shot.

Amazingly enough, this advice also works really well with deer.
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Dear TRS: Sometimes when I'm speaking to someone on the phone, and he's giving instructions or telling me something, I won't understand what he's saying, but I'd rather just say, "Mmmhhhhmmmm. Yeah, OK" than find out what he said. After I hang up, I think, "Gosh I wonder what he said." Why do I do that?

Sincerely,

A Bochur in Bobov/Belz/Brergsass/Biala/Boston/Boyan/Bohush/Binding/Bonia/Bender
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Dear Bochur,

You know what you need? To clear out the wax in your ear. Or else you need some help becoming more assertive. Try becoming a lawyer, and suing the girl we dealt with in the previous question- who knows, maybe you could even marry her!
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Dear TRS: What's your all time favorite Lipa song?

Sincerely,

Tom Dennis Fitzgerald
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Dear Brain,

That's like asking a father to pick the most precious of his children. Still, we all know that one kid always gets stiffed in the will, and in this case, I think I'd have to say that if there's one song I could never stand, it's Halelu off A Poshiter Yid. In Lipa's defense, he didn't write the song. On the other hand, he obviously loves it. Maybe it's like when the parents adopt a kid who turns out to be a serial murderer- they have to show it all the more love. Or maybe it has something to do with the moon and tides and such things. I really couldn't tell you.

Ask Heightsdeals.com

Dear Heightsdeals.com,

I’m looking for a solution to a slight problem I’m having right now. Basically, my pet goldfish died, and I don’t know what to do. It’s really sad, because I loved my pet goldfish like a brother, and now I just don’t know what to do! I remember all the good times, when we used to just sit there and stare at each other. I remember nursing him back to health when he was sick, pouring just a drop of chicken soup into his fishbowl to ensure he’d get better. Unfortunately though, this only lead to his death, as the hot soup scalded him. I immediately pulled him out and put on first aid cream, but I guess it was too late, and I was left bereft of my only friend. What shall I do?

Sincerely,

Johnson

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Dear Johnson,

I’m very sorry to hear about the loss of your fish; I’ve had pets myself, and I know how attached people get to the little critters. Might I suggest you go for a new pet that requires a little less personal love and care? The LG CU920 Vu has this really cool feature that allows you to have a fish on your front screen. You can play with this fish and everything, and it’ll never even get sick! Probably a good thing, because cellphones appreciate chicken soup even less than goldfish.

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Dear Heightsdeals.com

Two weeks ago I got ripped off resigning with one of the big cellphone companies, and now I don’t know what to do. I wanted a cool new phone, so I spent all my money on yet another two year plan, plus I had to pay big bucks for the cellphone. The customer service is terrible, and I feel confused, frustrated, and lonely. Whatever shall I do?

Sincerely,

Carl

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Deal Carl,

Here at Heightsdeals.com we hear many heartbreaking stories like your own. The saddest is when, as in your case, the customer reups with his phone company- fool me once, shame on you, fool me twice, shame on who? Don’t worry though, there’s no need to panic. Most of the major carriers have thirty day money back guarantees, and once you’re rid of the waste you can move on to bigger and greater things, like a brand new unlocked cell phone which you can use with many different cell companies. Might I suggest the MotoRoker EM30? You’ll be able to listen to all your favorite music and call your friends to let them know how much you’re enjoying your new phone. Best of all, you’ll be emboldening freedom-seekers around the world and striking a blow for justice and opportunity. Sounds noble and far-fetched? Perhaps, but for every action there is an equal and opposite reaction, and with your help we can bring redemption to the world’s repressed cellphone using millions.

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Dear Heightsdeals.com,

I haven’t had a big break in a long time. Everywhere I turn I’m besieged by doubts. Can I do succeed, can I make a way for myself in life, can I truly live up to my great potential? I just don’t know what to do. Please help.

Sincerely,

Eli

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Dear Eli,

You sound a bit depressed, which is understandable, because you obviously haven’t had any reason to be happy lately. It’s been two and a half weeks since New Years, and even longer since you played in a meaningful football game. Whether it was your supporting cast or your leg that let you down, it’s now time for a change. Change is good. Change can help you. All right, a new defensive coordinator probably won’t do much to help your people catch the balls they’re currently dropping, but perhaps we can help them. After all, what’s the real issue here? Communication, or lack thereof. The receivers just aren’t feeling your vibes, and they’re not catching your balls. Or maybe the issue is that your overthrowing. Or that your best receiver is in jail. Maybe. If the issue is the lack of communication, then we have just the thing for you- a brand new Sidekick LX. You can call or text or chat down field and finally start throwing some touchdowns.

Dear TRS: Happy?

That's right folks, it's time for another exciting edition of Dear TRS, the quiz show you get to play along with too! Enjoy.
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Dear TRS: Why have you become all holy lately?

Sincerely,

Karl

Dear Karl,

Censorship is an interesting phenomenon. Some people are censored by the government, others by their own conscience, others by their own lack of restraint. The punishment for trying to avoid censorship varies as well. In some places the attitude is one of benevolent allowance-try us as much as you want, ain't nothing getting through... but ten points for trying! In other places they not only control what you say but punish you for trying to say it. In those places it's, "What? You dare trifle with me? Guards, go break his legs!" Neither of these approaches really accomplishes what it is that the censor is trying to effect-his job is not simply to remove objectionable material, but rather to remove the conditions that allow for the material to ever get to him in the first place. All right, if the censor is just looking for entertainment then he can have plenty of that with the status quo, but then he's not really the ideal censor. No, what you're really looking for is a guy who can convince the producer of the objectionable material that what he's doing is wrong. Not illegal, but wrong. And yeah, I know it's asking a lot of a pencil pusher sitting in some anonymous government highrise somewhere in the middle of the bible belt to radically affect some radical hippy cross-dressing dudes wearing floral print dresses and floppy straw hats with little pins that say "Free Tibet!" on 'em to make much of a difference, but trust me, it is possible. How do they do it, this select band of censors with soul, this prized group of bowdlerizers with the breath of divine life flowing through their parched bones (for how can a person whose whole being is dedicated to the muzzling of their fellows have anything but the driest of Ezekiel valley special?), these suppressionists with a sense of mission, a belief in the ultimate goal that has eluded so many?

The answer is very simple. Guilt.
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Dear TRS: Why do they use phones to call in guys from the bullpen? Wouldn't texting be much easier?

Sincerely,

Snert

Dear Snert,

Even better, they could tweet it! Just imagine, the manager tweets, "@Orlando Mercado Joe Mauer just walked, we need @Darren Oliver in here pronto!" And the tweet back? "@Mike Scioscia the fireman cometh!"
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Dear TRS: Is there any specific reason why the Twins had to blow the game tonight?

Sincerely,

Joe and Jason

Dear Joe and Jason,

Well, you two certainly did everything that could be expected of you. It's been a tough road trip, eh?
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Dear TRS: Why the heck does Iran have twelve vice presidents?

Sincerely,

Karl (again)

Dear Karl,

The president must have a lot of vices.
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Dear TRS: Since when did it become socially acceptable to roll hoops?

Sincerely,

Mackenzi Van Engelenhoven

Dear Mackenzi Van Engelenhoven, let me first tell you that I really appreciate your question. No, really, I do.
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Dear TRS:

I'm very insulted if my name doesn't appear at least twice in every publication in America,

Sincerely,

Barack H. Obama
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Dear Mr. Obama, happy?
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And that folks is the end of the line. Did you enjoy playing the quiz show you get to play along with too?

Dear TRS: A roaring success!

Once again, folks, you're privileged to read another fascinating edition of Dear TRS. How about a brief preface from today's Shulchan Oruch? So let's say you have a cow in a room, and there's a lion nail in the cow's back. There also happens to be a lion having a nap outside the room. Is the cow kosher? If the lion nail came from the lion, then the cow isn't kosher, it's a treifah. So what's the safek? Maybe the lion never went into the room. And even if it did, maybe it got a nail stick in the wall, and then the cow walked over to scratch it's back, and the nail got implanted in the cow, in which case the cow is still kosher. The Shulchan Oruch rules that the cow is kosher because it's a sfek sfekah.

The obvious question is, why? There would seem to only be one sfekah here, whether the lion put the nail in or not. Otherwise, how'd the nail get there if the lion never came in the room? (At this point in shiur I suggested aliens, but Rabbi Chaim Schapiro wasn't too taken with my answer). Another interesting factoid that emerged from today's shiur is that lions have poison in their claws! Who knew? It would also appear that even the Darchei Moshe (the Ramah) couldn't answer this question, so we're in good company.

The point of this was to demonstrate that I don't know all the answers (surprise, surprise) to all these genuine questions. On that note, here goes.

Dear Sir:

What is the purpose of the comment field on a blog?

sincerely,

170 comments on my shirt today :-)
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Dear anon:

To leave comments, of course.
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Dear Sir:
Why penguins? Why not parrots or some other exotic bird?

Sincerely,

Colorful Bochur
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Dear uniform-challenged young man:

Penguins can swim underwater (mikveh), and they wear tuxedos. Could there be a better role model for our youth?
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Dear Sir:

Which is faster, to New York or by train?

Sincerely,

Joseph Biden
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Dear foot-in-mouth:

I prefer aeroplanes, myself.
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Dear Sir:

Please rephrase the following sentence so that it doesn't end with a preposition:
Land is not worth risking your life for.

Sincerely,

The Almighty Editor (retired)
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Dear crotchety baldy:

How about, "Yes it is."?
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Dear Sir:

I am a crocodile. I stole a child. I told the father that I would give it back if the father could accurately answer the following question:

Will I (the crocodile) give back the child? The father guessed that I would not return the child. Now what should I do?

Crying crocodile tears, yours do I remain,

Mr. Croc
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Dear Mr. Croc:

Have you ever considered investing in 240,00 pairs of crocs, five dollars each, for sale outside of the United States of America? The proceeds would allow the father to buy a new child to replace the one you ate, and that child to buy a new father to replace the one you ate for dessert.
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Dear Sir:

How do you deal with a Big Meanie that is controlling your life and using your labor? Do you run away? Do you stop working? Do you confront them?

Thanks,

A simple slave
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Dear A Poshite Kabbalos Olnik:

Polish her floors (very early) in the morning, and when she wakes up she'll walk on them, slip, hit her head hard on the spotless floor, and have peculiar brain damage, such that she will lose her previous character and become a happy, healthy, contributing member of society once again.
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Dear Sir:

Is one allowed to dance around the bimah on Shabbos during the sefira?

Sincerely,

Permission to tango
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Dear Permission to engage in highly immoral activity:

What makes you think you can dance on any day of the year? This is the kind of leitzonus which is bringing the Jewish people into disrepute among the nations.
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Dear Sir:

If half of my French toast is runny and the other half is burnt, what changes in cooking should the cook implement?

Sincerely,

Butter side up
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Dear Butter side up:

Have you ever considered coming to the Rabbinical College of America, where Dovid Solomon makes a decent french toast every week?
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Dear Sir:

Is one allowed to eat a pas Yisroel cookie shaped like Harry Potter?

Sincerely,

Concerned Hogwarts parent
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Dear Vernon Dursley:

Is it yoshon?
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Dear Sir:

Why are literal penguins forbidden to bring into the zoos where figurative penguins (i.e. bochurim) have their habitats?

Sincerely,

Conservationist
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Dear tree-hugging liberal:

The bochurim's guano might prove too much for the penguins.
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Dear Sir:

If the measure of a philosopher is the quality of his hamburgers, what about vegetarian philosophers? Or philosophers who prefer hot dogs?

Sincerely,

Hugh Akston's Brother in law
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Dear One of the last great advocates of reason:

Well, what about vegetarian philosophers? Is nisht kein stirah!
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Dear Sir:

Why isn't a fish a cow?

Sincerely,

The other 4
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Dear plus 1:

Because if it was, all hell would break loose.
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Dear TRS: The oddly calmed edition

R' Shmuel Munkes once invented a mouse poison which he guaranteed would kill all and any mice. A chassid bought it, and came a few days later to complain, "You're poison doesn't work! The mice won't touch it!" R' Shmuel said, "Very simple. First you catch the mouse, then you make it swallow the poison, and then it dies." The Chassid said, "But once I catch the mouse, I don't need the poison anymore!" R' Shmuel said, "Ain lecha nami."

With that story in mind, it's time for a wholly original Dear TRS. Yup.

Dear Sir:

Why do penguins/bochurim, while on the street, spontaneously burst into song? It's unnerving.

Signed,

Alarmed
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Dear Alarmed,

Your question is very important to us, and as soon as we finish humming this tune we'll attempt to get back to you.
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Dear Sir:

I really must know, why is a fish?

Signed,

New Age Feminist
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Dear New Age,

Because if it wasn't, then what would it be?
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Dear Sir:

If even snags admit they are allowed to sing during sfira why do they prohibit recorded singing (a capella) as "too much like music"?

Sincerely,

Hypocrisy Rocks
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Dear Hypocritical,

One of the most fundamental elements of snagginess of learning not to question the Gedolim. When the gedolim say something, you should listen. In other words, the words of the Gedolim to you must be the law. What I'm trying to say is, the Gedolim must be listened to and trusted in implicitly.

Having said that, I would like to point out that in fact only a capella music that is able to be listened to is banned from being listened to. Therefore, any non-listenable music is permitted to be listened to.
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Dear Sir:

Will you join my organization Morons And Dumkopfs Negating Endlessly Stagnating 'Stereotypes' (MADNESS) We have several guidelines for our members to follow. In the interests of furtherance of multiculturalism will you agree never to speak to a Muslim lest you offend his or her religious sensibilities? Furthermore, will you agree never to take a picture of a young sfardi chareidi lest it be misinterpreted as an image of Muhammad may he rest in pieces?

Sincerely,

A.P Manson
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Dear A.P. Manson

At first I was very excited to join your organization, but then I realized that you made fun of the prophet Muhammad, and I resolved to blow you up.
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Dear Sir:

Don't you know that it is the height of shamelessness for an advice columnist to solicit questions?

yours truly,

Heckler
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Dear Heckler,

I merely follow in the best traditions of my predecessors who always have a mailing address by their columns. Besides, wouldn't you think it weird if I had an advice column and no one to address the address to?
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Sincerely to all, TRS

Dear TRS: Reality sets in

That's right folks, it's time for another exciting edition of ask the RS. Incidentally, all of these are real questions, sent in by real people. Scary, I know. Here we go:

Dear Sir:

Can you think of an English rhyme to aid baalei tshuva in understanding the talmudic and practical concept of "der oilam's ah goilem?"
sincerely,

Shliach to the poets-in-residence
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Dear Shliach to the poets-in-residence,

Are you trying to suggest that the masses are asses? And not even the asses of Rebbi Pinchas Ben Yair?
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Dear Sir:
Is the prohibition of music in effect on hallel days that occur during sfira? If so does yom ha'atzmaut (known to certain chagas kreizin as yoim huhhatzomos) count?

What about stuff that is technically produced on instruments but is not music by any sane definition? (Insert singer/group you dislike)
sincerely,

Metal Fan
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Dear Metal Fan,

The answer to your first question is that if you're willing to suspend rational thought and hold that you can't listen to whatever it is you're not listening to then the same would apply on hallel days as well, obviously excepting the 5th of Iyar, when it's a mitzvah to play Hatikvah on loudspeakers from a Mitzvah Tank in Williamsburg.

Any music which is not music by any sane definition shouldn't be listened to anyway, so what's the question? You mean if you're of a snaggish disposition and have masochistic tendencies?
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Dear Sir:

What is the fundamental question of integral calculus and what does it have to do with differential calculus? And oh yeah, what is the point of that little carrot shaped button on my blue calculator?

Sincerely,

Mathematically Mystified
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Dear Mathematically Mystified,

I.

Let f be a continuous real-valued function defined on a closed interval a,">b. If F is the function defined for x in a,">b by

$F(x)\; =\; \backslash int\_a^x\; f(t)\backslash ,\; dt$

then

$F\text{'}(x)\; =\; f(x)\backslash ,$

for every x in a,">b.

II.

Let F be a continuous real-valued function defined on a closed interval a,">b. If f is the function such that

$f(x)\; =\; F\text{'}(x)\backslash ,$ for all x in a,">b

then

$\backslash int\_a^b\; f(x)\; dx\; =\; F(b)\; -\; F(a)$.

Corollary

Let F be a real-valued continuous function defined on a closed interval a,">b. If f is the function defined by

$f(x)\; =\; F\text{'}(x)\backslash ,$ for all x in a,">b

then

$F(x)\; =\; \backslash int\_a^x\; f(t)\; dt\; +\; F(a)$

and

$f(x)\; =\; \backslash frac\{d\}\{dx\}\; \backslash int\_a^x\; f(x)\; dx$.

Proof

Part I

It is given that

$F(x)\; =\; \backslash int\_\{a\}^\{x\}\; f(t)\; dt$

Let there be two numbers x₁ and x₁ + Δx in a,">b. So we have

$F(x\_1)\; =\; \backslash int\_\{a\}^\{x\_1\}\; f(t)\; dt$

and

$F(x\_1\; +\; \backslash Delta\; x)\; =\; \backslash int\_\{a\}^\{x\_1\; +\; \backslash Delta\; x\}\; f(t)\; dt$.

Subtracting the two equations gives

$F(x\_1\; +\; \backslash Delta\; x)\; -\; F(x\_1)\; =\; \backslash int\_\{a\}^\{x\_1\; +\; \backslash Delta\; x\}\; f(t)\; dt\; -\; \backslash int\_\{a\}^\{x\_1\}\; f(t)\; dt\; \backslash qquad\; (1)$.

It can be shown that

$\backslash int\_\{a\}^\{x\_1\}\; f(t)\; dt\; +\; \backslash int\_\{x\_1\}^\{x\_1\; +\; \backslash Delta\; x\}\; f(t)\; dt\; =\; \backslash int\_\{a\}^\{x\_1\; +\; \backslash Delta\; x\}\; f(t)\; dt$.

(The sum of the areas of two adjacent regions is equal to the area of both regions combined.)

Manipulating this equation gives

$\backslash int\_\{a\}^\{x\_1\; +\; \backslash Delta\; x\}\; f(t)\; dt\; -\; \backslash int\_\{a\}^\{x\_1\}\; f(t)\; dt\; =\; \backslash int\_\{x\_1\}^\{x\_1\; +\; \backslash Delta\; x\}\; f(t)\; dt$.

Substituting the above into (1) results in

$F(x\_1\; +\; \backslash Delta\; x)\; -\; F(x\_1)\; =\; \backslash int\_\{x\_1\}^\{x\_1\; +\; \backslash Delta\; x\}\; f(t)\; dt\; \backslash qquad\; (2)$.

According to the mean value theorem for integration, there exists a c in x₁,">x₁ + Δx such that

$\backslash int\_\{x\_1\}^\{x\_1\; +\; \backslash Delta\; x\}\; f(t)\; dt\; =\; f(c)\; \backslash Delta\; x$.

Substituting the above into (2) we get

$F(x\_1\; +\; \backslash Delta\; x)\; -\; F(x\_1)\; =\; f(c)\; \backslash Delta\; x\; \backslash ,$.

Dividing both sides by Δx gives

$\backslash frac\{F(x\_1\; +\; \backslash Delta\; x)\; -\; F(x\_1)\}\{\backslash Delta\; x\}\; =\; f(c)$.

Notice that the expression on the left side of the equation is Newton's difference quotient for F at x₁.

Take the limit as Δx → 0 on both sides of the equation.

$\backslash lim\_\{\backslash Delta\; x\; \backslash to\; 0\}\; \backslash frac\{F(x\_1\; +\; \backslash Delta\; x)\; -\; F(x\_1)\}\{\backslash Delta\; x\}\; =\; \backslash lim\_\{\backslash Delta\; x\; \backslash to\; 0\}\; f(c)$

The expression on the left side of the equation is the definition of the derivative of F at x₁.

$F\text{'}(x\_1)\; =\; \backslash lim\_\{\backslash Delta\; x\; \backslash to\; 0\}\; f(c)\; \backslash qquad\; (3)$.

To find the other limit, we will use the squeeze theorem. The number c is in the interval x₁,">x₁ + Δx, so x₁ ≤ c ≤ x₁ + Δx. Also, $\backslash lim\_\{\backslash Delta\; x\; \backslash to\; 0\}\; x\_1\; =\; x\_1$ and $\backslash lim\_\{\backslash Delta\; x\; \backslash to\; 0\}\; x\_1\; +\; \backslash Delta\; x\; =\; x\_1$. Therefore, according to the squeeze theorem,

$\backslash lim\_\{\backslash Delta\; x\; \backslash to\; 0\}\; c\; =\; x\_1$.

Substituting into (3), we get

$F\text{'}(x\_1)\; =\; \backslash lim\_\{c\; \backslash to\; x\_1\}\; f(c)$.

The function f is continuous at c, so the limit can be taken inside the function. Therefore, we get

$F\text{'}(x\_1)\; =\; f(x\_1)\; \backslash ,$.

which completes the proof. (Leithold et al, 1996)

Part II

This is a limit proof by Riemann Sums. Let f be continuous on the interval a,">b, and let F be an antiderivative of f. Begin with the quantity

$F(b)\; -\; F(a)$.

Let there be numbers x₁ thru x_n such that

$F(b)\; -\; F(a)\; =\; F(x\_n)\; -\; F(x\_0)\; \backslash ,$.

Now, we add each F(x_i) along with its additive inverse, so that the resulting quantity is equal:

& = & F(x_n)\,-\,F(x_{n-1})\,+\,F(x_{n-1})\,+\,\ldots\,-\,F(x_1)\,+\,F(x_1)\,-\,F(x_0) \, \end{matrix} The above quantity can be written as the following sum:

$F(b)\; -\; F(a)\; =\; \backslash sum\_\{i=1\}^n-\; F(x\_\{i-1\})\backslash qquad\; (1)$

Here we employ the Mean Value Theorem. In brief, it is as follows:

Let f be continuous on the closed interval a,">b and differentiable on the open interval (a, b). Then there exists some c in (a, b) such that

$f\text{'}(c)\; =\; \backslash frac\{f(b)\; -\; f(a)\}\{b\; -\; a\}$.

It follows that

$f\text{'}(c)(b\; -\; a)\; =\; f(b)\; -\; f(a)\; \backslash ,$.

The function F is differentiable on the interval a,">b; therefore, it is also differentiable and continuous on each interval x_i-1. Therefore, according to the Mean Value Theorem (above),

$F(x\_i)\; -\; F(x\_\{i-1\})\; =\; F\text{'}(c\_i)(x\_i\; -\; x\_\{i-1\})\; \backslash ,$.

Substituting the above into (1), we get

$F(b)\; -\; F(a)\; =\; \backslash sum\_\{i=1\}^n-\; x\_\{i-1\})$.

As the derivative of the antiderivative is the original function, $F\text{'}(c\_i)\; =\; f(c\_i)$. Also, $x\_i\; -\; x\_\{i-1\}$ can be expressed as $\backslash Delta\; x$ of partition $i$.

$F(b)\; -\; F(a)\; =\; \backslash sum\_\{i=1\}^nx\_i)\backslash qquad\; (2)$

Notice that we are describing the area of a rectangle, with the width times the height, and we are adding the areas together. Each rectangle, by virtue of the Mean Value Theorem, describes an approximation of the curve section it is drawn over. Also notice that $\backslash Delta\; x\_i$ does not need to be the same for any value of $i$, or in other words that the width of the rectangles can differ. What we have to do is approximate the curve with $n$ rectangles. Now, as the size of the partitions get smaller and n increases, resulting in more partitions to cover the space, we will get closer and closer to the actual area of the curve. By taking the limit of the expression as the norm of the partitions approaches zero, we arrive at the Riemann integral. That is, we take the limit as the largest of the partitions approaches zero in size, so that all other partitions are smaller and the number of partitions approaches infinity. So, we take the limit on both sides of (3). This gives us

$\backslash lim\_\{\backslash |\; \backslash Delta\; \backslash |\; \backslash to\; 0\}\; F(b)\; -\; F(a)\; =\; \backslash lim\_\{\backslash |\; \backslash Delta\; \backslash |\; \backslash to\; 0\}\; \backslash sum\_\{i=1\}^nx\_i)\backslash ,dx$

The expressions F(b) and F(a) are not dependent on ||Δ||, so the limit on the left side remains F(b) - F(a).

$F(b)\; -\; F(a)\; =\; \backslash lim\_\{\backslash |\; \backslash Delta\; \backslash |\; \backslash to\; 0\}\; \backslash sum\_\{i=1\}^nx\_i)$

The expression on the right side of the equation defines an integral over f from a to b. Therefore, we obtain

$F(b)\; -\; F(a)\; =\; \backslash int\_\{a\}^\{b\}\; f(x)\backslash ,dx$

which completes the proof.

Happy?

In answer to your second question, "What's up Doc?"
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Dear Sir:

My recently engaged friend was appointed to oversee all dorm-food preparation and thus is at her wits end. How might I go about telling her that raw eggs mixed with mushy bananas doesn't create ice cream, without losing my head?

Sincerely,

A'feared of Wrath

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Dear A'feared of Wrath

Just give her this simple recipe, and mention that TRS is now accepting donations:

Blend 6 very ripe bananas until smooth. Add 2 egg yolks and 3/4 cup of ground nuts, filberts, or almonds. Blend for one minute. Beat 4 egg whites until stiff. Mix slowly into banana mixture with wooden spoon. Pour into a glass dish and spread remaining 1/4 cup nuts on top. Freeze at least 4 hours. When serving poor 1 teaspoon wine on each scoop or portion.

Serves 12
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Dear Sir:

My brother insists on not cutting his afro and I fear that by the end of sefira all hope, not to mention sight, will be lost. Do you think he's mind if I trim it during the night? Then again, it would make for a lovely sheitel...

Sincerely,

Distressed
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Dear Distressed,

Do I think he'll mind if you sin against all that is holiness and sacred? Of course, locks for love is a wonderful organization.
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Dear Sir:

What's a Chol Hamoed trip that will be enjoyable for a family aged 1.5 through 55?

Sincerely,

Even more desperate
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Dear Even more desperate,

What exactly do 1.5 year olds enjoy doing anyway? From what I can tell, they're the same happy whether here or there.
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Dear Sir:

Why is borscht in America made of beets and borscht in Russia made with cabbage?

Sincerely,

Ari
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Dear Ari,

Perhaps because Americans prefer sour cream nine times out of ten?
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And that's all folks!

Dear TRS: More advice for the massively massed masses

That's right folks, it's time for another exciting adventure with the TRS mailbag-and this time we actually have mail! Woohoo! Anyway, here goes:

Dear Sir:

I know that I'm not allowed to listen to non-Jewish music, so can I sing niggunim while I'm in the shower?

Sincerely,

Piously Pondering

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Dear Piously Pondering,

What are you talking about? Do you mean to say that all Jewish songs are niggunim? Or else only niggunim are Jewish music? Either way, I think that any holy music should be avoided whilst in the lavatory or its attendant functionaries. If you feel the need to sing, why not hum sung Avraham Fried tunes? Of course, if you feel the need for niggunim, there's always Breslov...

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Dear Sir:

There's a female friend of mine who rides the bus late at night in dangerous neighborhoods. What should I do to persuade her to cease this dangerous activity?

Sincerely,

No really, it's not me, it's my friend

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Dear No really, it's not me, it's my friend,

Tell your friend to get married and have her husband drive her around.

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Dear Sir:

I'm wondering which is more chassidish: to have your last chametz before Pesach be a hot cross bun from Breadsmith, or perhaps sushi from Byerlys?

Sincerely,

Insincere

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Dear Insincere,

Seeing as Byerlys hasn't made Kosher sushi the whole week it would appear that the better option would be the hot cross bun.

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Dear Sir:

Are you going to make another cheap joke at our glorious president's expense in order to wring some humor from this heretofore humorless exercise, or will you manage to restrain yourself?

Sincerely,

Avremel Shemtov

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Dear Avremel Shemtov,

Why was Barack Obama so desperate to become the President? So he could get free public housing!

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And a Kosher and most happy Pesach to you and yours.

Dear TRS: advice for the masses

This is the first installment of what I hope will be a regular feature on TRS: an advice column. And let's get right down to it.

Dear Sir:

My cow refuses to eat the grass put before him. And he constantly hits me too. And steals my mechanical pencil. And won't allow me to use his sefarim as a book holder. What do I do?

Sincerely,

Fish.
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Dear Fish,

Your cow refuses to eat the grass put before him? How absolutely ghastly. And physical abuse is certainly not cricket. Neither is theft. Perhaps though you might soften on your stance of misappropriation of property, and he might come around on his own. At the very least you could simply stop telling him the latest gossip regarding your family-he'd certainly fall very quickly for that ploy.

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Dear Sir:

Shmuley Boteach has a nasty habit of writing stupid things. How do I prevent this in the future?

Sincerely,

Someone's future son in law.
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Dear someone's future son in law,

Shmuley Boteach has made a living of writing incendiary copy and then backtracking faster than even I ever have. The man is positively obsessed with being politically correct, and can't bear the thought of looking like a fundamentalist. He's also a wonderful human being (that's to save myself from his libel-seeking lawyers). My advice is, stop reading his articles and instead read those of Meir Kahane, who is probably closer to your cup of white hot chocolate (from Second Cup, of course), though he isn't as entertaining, principally because he's been insufferably right lately, despite his current deceased status.

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Dear Sir:

Why is it okay for a Republican to root for Tiger Woods but not for Barack Obama?

Sincerely,

Randy Moss
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Dear Randy Moss,

Perhaps it's because the former gets the job done?

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Dear Sir:

Why is it that people think they can get away with writing nothing of substance if they can come up with a couple of cheap jokes and a few jibes at America's president?

Sincerely,

IJT
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Dear IJT,

Darling, I have no idea what you're talking about.

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And thus concludes our first edition of whatever it is we'll be calling it in the future. Go us!