Question

Evaluating $\int_{x=0}^{1} \frac{\cos^2x}{\sqrt{x}}$ with Taylor series

score 93 · Answer 1 · 2026-04-07 01:53:16

93

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Evaluating $\int_{x=0}^{1} \frac{\cos^2x}{\sqrt{x}}$ with Taylor series

Published on 07 Apr 2026 - 1:53

score 105 · Answer 2 · 2020-03-15 11:20:21

105

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Evaluate $\sum_{r=1}^{\infty} \frac{1 \cdot 3 \cdot \ldots (2r-1)}{r!}\left(\frac{2}{5} \right)^{r}$

Published on 15 Mar 2020 - 11:20

score 119 · Answer 3 · 2026-03-28 10:56:17

119

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the Laurent series of $f(z)=\cos \frac {z}{z+1}$ on $0<|z-1|<\infty$

Published on 28 Mar 2026 - 10:56

score 263 · Answer 4 · 2026-04-08 03:25:33

263

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How to simplify the power series $\sum_{k=0}^{n-1}\frac{x^k}{k!}$?

Published on 08 Apr 2026 - 3:25

score 67 · Answer 5 · 2020-03-17 17:33:15

67

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Find the power series of $f(x) = \frac{e^{-x}}{x}$ using the power series of a parent function centered at $0$. How can I do this?

Published on 17 Mar 2020 - 17:33

score 54 · Answer 6 · 2020-03-17 20:13:07

54

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Expanding $(1+x/j)^{-1}(1+1/j)^{x}$

Published on 17 Mar 2020 - 20:13

score 216 · Answer 7 · 2026-04-03 21:20:26

216

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Intuitive motivation for limit computations

Published on 03 Apr 2026 - 21:20

score 239 · Answer 8 · 2026-03-26 22:17:41

239

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Taylor-like bound for the matrix exponential tr(exp(X))

Published on 26 Mar 2026 - 22:17

score 100 · Answer 9 · 2020-03-18 16:43:41

100

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Prove that $ \sum \limits_{n=1}^{\infty} \frac{n}{(n+1)^{(n+2)} (n+2)!}(-1)^{(n+1)} = \frac{23}{24} - \frac 2 3 \sqrt 2 $

Published on 18 Mar 2020 - 16:43

score 80 · Answer 10 · 2020-03-18 17:18:17

80

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Procedure in Taylor series - Understanding derivation

Published on 18 Mar 2020 - 17:18

score 64 · Answer 11 · 2020-03-18 17:50:30

64

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Proving $\sum_{k=1}^{\infty}\frac{x^k}{k}=-\ln(x+1)$

Published on 18 Mar 2020 - 17:50

score 85 · Answer 12 · 2026-04-06 10:56:33

85

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Proving that $e^x \geq \sqrt{x}$ for all $x\geq0$

Published on 06 Apr 2026 - 10:56

score 72 · Answer 13 · 2020-03-19 16:37:17

72

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Complex Taylor Series expansion - basic examples with radius of convergence

Published on 19 Mar 2020 - 16:37

score 35 · Answer 14 · 2026-03-25 03:04:06

35

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What's the meaning of ($x^2$) when we compute a Taylor's polynomial?

Published on 25 Mar 2026 - 3:04

score 744 · Answer 15 · 2026-03-30 03:56:46

744

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Use Taylor series to compute $\lim\limits_{x \to 0} \left( \frac{1}{\sin(x)}- \frac{1}{x} \right) $

Published on 30 Mar 2026 - 3:56

List Question

Evaluating $\int_{x=0}^{1} \frac{\cos^2x}{\sqrt{x}}$ with Taylor series

Evaluate $\sum_{r=1}^{\infty} \frac{1 \cdot 3 \cdot \ldots (2r-1)}{r!}\left(\frac{2}{5} \right)^{r}$

the Laurent series of $f(z)=\cos \frac {z}{z+1}$ on $0<|z-1|<\infty$

How to simplify the power series $\sum_{k=0}^{n-1}\frac{x^k}{k!}$?

Find the power series of $f(x) = \frac{e^{-x}}{x}$ using the power series of a parent function centered at $0$. How can I do this?

Expanding $(1+x/j)^{-1}(1+1/j)^{x}$

Intuitive motivation for limit computations

Taylor-like bound for the matrix exponential tr(exp(X))

Prove that $ \sum \limits_{n=1}^{\infty} \frac{n}{(n+1)^{(n+2)} (n+2)!}(-1)^{(n+1)} = \frac{23}{24} - \frac 2 3 \sqrt 2 $

Procedure in Taylor series - Understanding derivation

Proving $\sum_{k=1}^{\infty}\frac{x^k}{k}=-\ln(x+1)$

Proving that $e^x \geq \sqrt{x}$ for all $x\geq0$

Complex Taylor Series expansion - basic examples with radius of convergence

What's the meaning of ($x^2$) when we compute a Taylor's polynomial?

Use Taylor series to compute $\lim\limits_{x \to 0} \left( \frac{1}{\sin(x)}- \frac{1}{x} \right) $

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