rar

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724

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Self-Studying mathematics.

Currently reading:
Apostol, Calculus, Volumes I & II
Hardy & Wright, An Introduction to the Theory of Numbers
Hoffman & Kunze, Linear Algebra
Munkres, Topology
Enderton, Elements of Set Theory

	1,284 reputation	bio	website		visits	member for	1 year, 4 months
724 badges		location	San Francisco, CA		seen	2 hours ago

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13 Questions

views newest activity votes

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answers

kviews

What makes elementary functions elementary?

mar 1 at 21:15 imranfat 586

votes

answers

940

views

Must we use induction to prove a statement for all integers

soft-question proof-strategy induction

apr 26 '12 at 15:57 rar 1,284

votes

answers

kviews

Is Mega Millions Positive Expected Value?

probability recreational-mathematics

apr 14 '12 at 9:27 rar 1,284

votes

answer

357

views

Exercise 26 from Apostol's Calculus (p. 209, parts (c) & (d)))

calculus

mar 21 '12 at 15:02 rar 1,284

votes

answers

255

views

Prove that $\left|\int_a^b f(x) dx - (b-a) f(a) \right| \leq \frac{(b-a)^2}{2}$ when $f$ satisfies $|f(u)-f(v)|\leq |u-v|$

calculus analysis

may 17 at 10:44 Argha 1,519

votes

answer

266

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Apostol Calculus, Volume I, Chapter 8.7, Exercises 9 & 10 (p. 320)

calculus differential-equations

apr 23 '12 at 22:57 David Mitra 41.8k

votes

answer

104

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Calculating $f(0), f'(0), f''(0)$ for a function $f$ satisfying $\lim_{x \to 0} (1 + x + f(x)/x)^{1/x} = e^3$.

calculus limit

apr 10 '12 at 21:06 Did 107k

votes

answers

196

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How to prove $\int_0^1 \frac{1+x^{30}}{1+x^{60}} dx = 1 + \frac{c}{31}$, where $0 < c < 1$

calculus taylor-expansion

apr 5 '12 at 1:11 copper.hat 29.7k

votes

answers

105

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Trying to find $\lim_{x \to 0} \frac{x - \sin x}{(x \sin x)^{(3/2)}}$ using L'Hopital's

calculus limit

jun 23 '12 at 11:42 Chris's wise sister 11.6k

votes

answers

512

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Bound for error term in Taylor expansion of $\arctan x$.

calculus taylor-expansion

apr 5 '12 at 1:07 rar 1,284

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answers

views

Computing $f(x)$ if $\int_1^{xy} f(t) dt = y \int_1^x f(t) dt + x\int_1^y f(t) dt$ and $f(1) = 3$

calculus

mar 24 '12 at 21:51 David Mitra 41.8k

votes

answer

179

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Proving equivalent form of the mean-value theorem for derivatives

calculus derivatives

mar 16 '12 at 0:09 David Mitra 41.8k

vote

answers

258

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Apostol Calculus, Volume I, Chapter 7.11, Problem 31 (p. 291), $o$-notation

calculus

apr 9 '12 at 14:30 rar 1,284