Question

Approximation of a ratio

score 1.3k · Answer 1 · 2014-10-07 16:17:49

1.3k

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Approximation of a ratio

Published on 07 Oct 2014 - 16:17

score 74 · Answer 2 · 2026-03-27 00:59:54

74

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Why is this true? $\forall a\in(1,\infty), B\in(0,\infty), x\in(0,\infty) : a^x\geq \left(\frac{ex\ln(a)}{B}\right)^{B}$

Published on 27 Mar 2026 - 0:59

score 271 · Answer 3 · 2014-10-07 21:43:13

271

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Book Request: Taylor's Theorem for functions $f: \Bbb R^n \to \Bbb R^m$

Published on 07 Oct 2014 - 21:43

score 107 · Answer 4 · 2026-03-30 00:24:37

107

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Are the Taylor polynomials of a function the results of a minimization problem?

Published on 30 Mar 2026 - 0:24

score 38 · Answer 5 · 2026-03-26 08:00:26

38

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Can anyone explain how to show the finite difference equation $y'_{0}=\frac{y_{1}-y_{-1}}{2h} + O(h^{2}).$?

Published on 26 Mar 2026 - 8:00

score 305 · Answer 6 · 2014-10-10 21:00:25

305

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Help finding n-order Maclaurin polynomial

Published on 10 Oct 2014 - 21:00

score 50 · Answer 7 · 2014-10-11 16:39:19

50

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The $n$th-derivative of $q(x) = x^4 - 8x^3 - 4x^2 + 3x - 2$, where $n \le 4$

Published on 11 Oct 2014 - 16:39

score 28 · Answer 8 · 2014-10-11 23:41:38

28

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Simplification of a series so that it converges to a given function

Published on 11 Oct 2014 - 23:41

score 35 · Answer 9 · 2014-10-12 22:55:59

35

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Expand with a Taylor formula $\frac{2+x}{x^2+2x+2}$ near the $x_0 = -1$

Published on 12 Oct 2014 - 22:55

score 147 · Answer 10 · 2014-10-13 18:44:16

147

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Taylor Polynomial of $f(x)=\cos(x)\cdot\sin(x)$

Published on 13 Oct 2014 - 18:44

score 366 · Answer 11 · 2014-10-14 02:18:31

366

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Maclaurin series expansion of $\frac{1}{(1+x)^n}$

Published on 14 Oct 2014 - 2:18

score 1.8k · Answer 12 · 2014-10-14 05:18:45

1.8k

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Sum Representation of log(1 + x)

Published on 14 Oct 2014 - 5:18

score 189 · Answer 13 · 2026-03-26 14:34:37

189

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MacLaurin of the Third-degree in sin(ax)cos(b*x) at given values

Published on 26 Mar 2026 - 14:34

score 77 · Answer 14 · 2014-10-15 03:17:08

77

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Use the power series representations of functions to find the taylor series of $\frac{1}{5+x'}$ at center = -6.

Published on 15 Oct 2014 - 3:17

score 306 · Answer 15 · 2026-03-30 11:12:30

306

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Multiple representations of ternary expansions of numbers

Published on 30 Mar 2026 - 11:12

List Question

Approximation of a ratio

Why is this true? $\forall a\in(1,\infty), B\in(0,\infty), x\in(0,\infty) : a^x\geq \left(\frac{ex\ln(a)}{B}\right)^{B}$

Book Request: Taylor's Theorem for functions $f: \Bbb R^n \to \Bbb R^m$

Are the Taylor polynomials of a function the results of a minimization problem?

Can anyone explain how to show the finite difference equation $y'_{0}=\frac{y_{1}-y_{-1}}{2h} + O(h^{2}).$?

Help finding n-order Maclaurin polynomial

The $n$th-derivative of $q(x) = x^4 - 8x^3 - 4x^2 + 3x - 2$, where $n \le 4$

Simplification of a series so that it converges to a given function

Expand with a Taylor formula $\frac{2+x}{x^2+2x+2}$ near the $x_0 = -1$

Taylor Polynomial of $f(x)=\cos(x)\cdot\sin(x)$

Maclaurin series expansion of $\frac{1}{(1+x)^n}$

Sum Representation of log(1 + x)

MacLaurin of the Third-degree in sin(ax)cos(b*x) at given values

Use the power series representations of functions to find the taylor series of $\frac{1}{5+x'}$ at center = -6.

Multiple representations of ternary expansions of numbers

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