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
fbe a continuous real-valued function defined on a closed interval a,">b. IfFis the function defined forxin a,">bby

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

- $F\text{'}(x)\; =\; f(x)\backslash ,$
- for every
xin a,">b.II.

### Corollary

LetFbe a real-valued continuous function defined on a closed interval a,">b. Iffis the function defined bythen

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

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

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

## Proof

### Part I

It is given that- $F(x)\; =\; \backslash int\_\{a\}^\{x\}\; f(t)\; dt$

*x*

_{1}and

*x*

_{1}+ Δ

*x*in a,">

*b*. So we have

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

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

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

- $\backslash int\_\{a\}^\{x\_1\}\; f(t)\; dt\; +\; \backslash int\_\{x\_1\}^\{x\_1\; +\; \backslash Delta\; x\}\; f(t)\; dt\; =\; \backslash int\_\{a\}^\{x\_1\; +\; \backslash Delta\; x\}\; f(t)\; dt$.
- (The sum of the areas of two adjacent regions is equal to the area of both regions combined.)

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

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

*c*in x

_{1},">

*x*

_{1}+ Δ

*x*such that

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

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

*x*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*x*_{1}.

*x*→ 0 on both sides of the equation.

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

*F*at

*x*

_{1}.

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

*c*is in the interval x

_{1},">

*x*

_{1}+ Δ

*x*, so

*x*

_{1}≤

*c*≤

*x*

_{1}+ Δ

*x*. 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,

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

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

*f*is continuous at

*c*, so the limit can be taken inside the function. Therefore, we get

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

### 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

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

*x*

_{1}thru

*x*

_{n}such that $a\; =\; x\_0\; <\; x\_n\; ="\; b.\; It\; follows\; that$

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

*F*(

*x*

_{i}) along with its additive inverse, so that the resulting quantity is equal:

- $\backslash begin\{matrix\}\; F(b)\; -\; F(a)\; \&\; =\; \&\; F(x\_n)\backslash ,+\backslash ,-F(x\_\{n-1\})\backslash ,+\backslash ,F(x\_\{n-1\})\backslash ,+\backslash ,\backslash ldots\backslash ,+\backslash ,+\; F(x\_1)\backslash ,-\backslash ,F(x\_0)\; \backslash ,\; \backslash \backslash $

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

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

Letfbe continuous on the closed interval a,">band differentiable on the open interval (a,b). Then there exists somecin (a,b) such thatIt follows that

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

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

*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),

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

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

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

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

*F*(

*b*) and

*F*(

*a*) are not dependent on ||Δ||, so the limit on the left side remains

*F*(

*b*) -

*F*(

*a*).

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

*f*from

*a*to

*b*. Therefore, we obtain

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

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

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:

Sincerely,

Distressed

--

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

Sincerely,

Even more desperate

--

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

--

Dear Ari,

Perhaps because Americans prefer sour cream nine times out of ten?

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And that's all folks!

## 16 comments:

thanx for teaching us math!!! (i didn't actually read it, but it looks complicated.)

I did read it. It

iscomplicated. There are much simpler ways of writing that which might even make sense. Then again, they don't look half so impressive.Oh, and the carrot thingy is for exponents.

yoish: don't worry, I didn't read it either.

Modeh: Carrots are for carrot cake, obviously.

How does that even answer the Calculus question?

It doesn't quite. He took a proof of the Fundamental theorem and pasted it in. As far as I can tell it isn't even much of a proof but I didn't actually slog through it. I have better things to do.

le7: How should I know?

Modeh: Exactly.

Why are there only 6 comments on this post?

(Now 7).

Because Pesach rather limits one's intnet time...by te way, that recipe sounds good.

le7: now 9.

sara: really? shocking!

and yeah, it is a real recipe.

Next time you want a fake Math theorem talk to a dilettante extraordinaire. I.e., find any Russian Jew. But to an untrained eye looks hilarious.

See, you would tell me it’s a question of taste, but I would answer that your funny posts are objectively funnier than supposedly funny posts of other supposedly funny supposedly frum bloggers.

I definitely second CA.

Re: math: it's not a fake math theorem! I have no idea what it means, but it's not fake.

re: humor: thanks, CA+le7

I meant fake math question. Or something like that. All math is real. Even the one proven wrong. It’s just that its source is on such spiritual levels that it cannot cloth itself in this world’s reality.

By the way, you should know that equation. And I should know what brocha to say on raw lemons. Neither of us is doing a good job.

I should know that equation? Why?

Nu, nu. You are a shliach of the Rebbe! (Said in the same tone as “I am captain Jack Sparrow!”)

Which tone would that be?

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