Question

Expanding an inverse trigonometric function into a power series

score 328 · Answer 1 · 2018-01-26 11:05:17

328

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Expanding an inverse trigonometric function into a power series

Published on 26 Jan 2018 - 11:05

score 63 · Answer 2 · 2026-04-09 15:42:50

63

Views

What is wrong in the following reasoning for calculate this limit

Published on 09 Apr 2026 - 15:42

score 312 · Answer 3 · 2026-04-10 19:20:13

312

Views

Calculating the limit of the sum.

Published on 10 Apr 2026 - 19:20

score 154 · Answer 4 · 2026-03-27 13:25:21

154

Views

Determine all real numbers $a$ for which the limit $\lim\limits_{x\to ∞ }a^nA^n$ exists and is non zero.

Published on 27 Mar 2026 - 13:25

score 143 · Answer 5 · 2026-03-24 22:13:59

143

Views

Evaluate the limit of series, Lebesgue integral

Published on 24 Mar 2026 - 22:13

score 150 · Answer 6 · 2026-03-24 22:01:59

150

Views

Compute $\lim\limits_{x\to0}\left(\frac{1}{x^4}-\frac{\int_0^{x^2}e^{-u^2}du}{x^6}\right)$ without L'Hopital rule nor Taylor

Published on 24 Mar 2026 - 22:01

score 51 · Answer 7 · 2026-04-06 11:30:41

51

Views

Show that a function is truly decreasing near a point $x_\circ$ if it's derivative is less than zero, using the $\varepsilon$-$\delta$-technique.

Published on 06 Apr 2026 - 11:30

score 175 · Answer 8 · 2026-03-24 22:01:55

175

Views

Find $f'(0)$ if $\frac{f(4h)+f(2h)+f(h)+f\left(\frac{h}{2}\right)+f\left(\frac{h}{4}\right)+f\left(\frac{h}{8}\right)+\cdots}{h}=64$

Published on 24 Mar 2026 - 22:01

score 2.3k · Answer 9 · 2026-04-10 19:39:05

2.3k

Views

Multi variable limit $\lim\limits_ {(x, y) \to (0, 0)} \frac {e^{xy} − 1} y$

Published on 10 Apr 2026 - 19:39

score 710 · Answer 10 · 2026-04-09 03:37:54

710

Views

Limit of Product of iid Random Variables

Published on 09 Apr 2026 - 3:37

score 52 · Answer 11 · 2018-01-27 08:33:06

52

Views

Proove that the only real constant such that the limit is $c=2$

Published on 27 Jan 2018 - 8:33

score 124 · Answer 12 · 2026-03-24 22:07:48

124

Views

Computing $\lim\limits_{x\to0}\int_0^x\frac{t^2}{(x-\sin x)\sqrt{a+t}}\,dt$ without L'Hopital

Published on 24 Mar 2026 - 22:07

score 73 · Answer 13 · 2026-03-25 07:16:34

73

Views

Let $\ell =\lim\limits_{x\to b}\frac{f(x)-cb}{g(x)-b^2}$then compute $c-\ell $.

Published on 25 Mar 2026 - 7:16

score 270 · Answer 14 · 2026-04-10 04:23:29

270

Views

Is infinitely small error the same as $0$ error?

Published on 10 Apr 2026 - 4:23

score 246 · Answer 15 · 2026-03-25 09:06:49

246

Views

Prove the convergence of $\sum\limits_{k=2}^\infty \frac 1 {(2k+1)(2k+5)}$

Published on 25 Mar 2026 - 9:06

List Question

Expanding an inverse trigonometric function into a power series

What is wrong in the following reasoning for calculate this limit

Calculating the limit of the sum.

Determine all real numbers $a$ for which the limit $\lim\limits_{x\to ∞ }a^nA^n$ exists and is non zero.

Evaluate the limit of series, Lebesgue integral

Compute $\lim\limits_{x\to0}\left(\frac{1}{x^4}-\frac{\int_0^{x^2}e^{-u^2}du}{x^6}\right)$ without L'Hopital rule nor Taylor

Show that a function is truly decreasing near a point $x_\circ$ if it's derivative is less than zero, using the $\varepsilon$-$\delta$-technique.

Find $f'(0)$ if $\frac{f(4h)+f(2h)+f(h)+f\left(\frac{h}{2}\right)+f\left(\frac{h}{4}\right)+f\left(\frac{h}{8}\right)+\cdots}{h}=64$

Multi variable limit $\lim\limits_ {(x, y) \to (0, 0)} \frac {e^{xy} − 1} y$

Limit of Product of iid Random Variables

Proove that the only real constant such that the limit is $c=2$

Computing $\lim\limits_{x\to0}\int_0^x\frac{t^2}{(x-\sin x)\sqrt{a+t}}\,dt$ without L'Hopital

Let $\ell =\lim\limits_{x\to b}\frac{f(x)-cb}{g(x)-b^2}$then compute $c-\ell $.

Is infinitely small error the same as $0$ error?

Prove the convergence of $\sum\limits_{k=2}^\infty \frac 1 {(2k+1)(2k+5)}$

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