Question

Approximation using the Taylor series

score 67 · Answer 1 · 2016-08-14 09:26:48

67

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Approximation using the Taylor series

Published on 14 Aug 2016 - 9:26

score 591 · Answer 2 · 2026-04-12 11:26:14

591

Views

Taylor expansion for square root

Published on 12 Apr 2026 - 11:26

score 63 · Answer 3 · 2026-04-01 21:37:21

63

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How can I show $(1+4e^2)^{1/2}\approx 1+2e^2$ for $e<<1$?

Published on 01 Apr 2026 - 21:37

score 81 · Answer 4 · 2016-08-15 17:50:24

81

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find $f^{(15)}(0)$ if $f = \frac{10x^2+12x+4}{(x+2) (x^2 +1)}$

Published on 15 Aug 2016 - 17:50

score 322 · Answer 5 · 2026-03-26 01:29:11

322

Views

Can the "radius of analyticity" of a smooth real function be smaller than the radius of convergence of its Taylor series without being zero?

Published on 26 Mar 2026 - 1:29

score 67 · Answer 6 · 2026-03-29 19:27:38

67

Views

Asymptotic expansion of $(ix+a)^{q}$ as $x\rightarrow\infty$

Published on 29 Mar 2026 - 19:27

score 467 · Answer 7 · 2026-04-11 22:37:24

467

Views

By using a geometric series and a factorisation, compute the first three terms of this given Taylor expansion

Published on 11 Apr 2026 - 22:37

score 1.2k · Answer 8 · 2016-08-16 16:54:37

1.2k

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How to deduce the radius of convergence of a rational function on the reals?

Published on 16 Aug 2016 - 16:54

score 46 · Answer 9 · 2026-04-11 02:12:43

46

Views

Trouble understanding the proof of Taylor expansion for one variable functions

Published on 11 Apr 2026 - 2:12

score 563 · Answer 10 · 2026-04-11 18:31:24

563

Views

Sum of series which is not Arithmetic Progression or Geometric Progression

Published on 11 Apr 2026 - 18:31

score 99 · Answer 11 · 2026-04-03 21:48:29

99

Views

Show $\frac{x}{\left(1+x^2\right)^{n}}\underset{{n\to +\infty}}{\sim} \frac{1}{x^{2n-1}}$ for every $x>1$

Published on 03 Apr 2026 - 21:48

score 91 · Answer 12 · 2026-04-03 21:49:59

91

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Prove that $f_n(x): x\in\mathbb{R}\mapsto \frac{x}{(1+x^2)^{n}}$ converges pointwise to null function

Published on 03 Apr 2026 - 21:49

score 104 · Answer 13 · 2016-08-19 14:20:53

104

Views

Show convergence of series using Taylor series: $\sum_{n=1}^{\infty}\left(e^{\frac1{\large\sqrt{n}}}-1-\frac1{\sqrt{n}} - \frac{1}{2n}\right)$

Published on 19 Aug 2016 - 14:20

score 298 · Answer 14 · 2026-04-12 08:50:18

298

Views

Recursive relation for power series of the exponential

Published on 12 Apr 2026 - 8:50

score 44 · Answer 15 · 2016-08-21 21:20:53

44

Views

Show $\frac{\sin(x)\cos^{n}(x)}{1-\cos(x)}\sim_{x\to 0^+}\frac{x}{\frac{x^2}{2}}$

Published on 21 Aug 2016 - 21:20

List Question

Approximation using the Taylor series

Taylor expansion for square root

How can I show $(1+4e^2)^{1/2}\approx 1+2e^2$ for $e<<1$?

find $f^{(15)}(0)$ if $f = \frac{10x^2+12x+4}{(x+2) (x^2 +1)}$

Can the "radius of analyticity" of a smooth real function be smaller than the radius of convergence of its Taylor series without being zero?

Asymptotic expansion of $(ix+a)^{q}$ as $x\rightarrow\infty$

By using a geometric series and a factorisation, compute the first three terms of this given Taylor expansion

How to deduce the radius of convergence of a rational function on the reals?

Trouble understanding the proof of Taylor expansion for one variable functions

Sum of series which is not Arithmetic Progression or Geometric Progression

Show $\frac{x}{\left(1+x^2\right)^{n}}\underset{{n\to +\infty}}{\sim} \frac{1}{x^{2n-1}}$ for every $x>1$

Prove that $f_n(x): x\in\mathbb{R}\mapsto \frac{x}{(1+x^2)^{n}}$ converges pointwise to null function

Show convergence of series using Taylor series: $\sum_{n=1}^{\infty}\left(e^{\frac1{\large\sqrt{n}}}-1-\frac1{\sqrt{n}} - \frac{1}{2n}\right)$

Recursive relation for power series of the exponential

Show $\frac{\sin(x)\cos^{n}(x)}{1-\cos(x)}\sim_{x\to 0^+}\frac{x}{\frac{x^2}{2}}$

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