Question

Why is $e^{\int_0^t A(s)} \mathrm{d} s$ a solution of $x' = Ax$ iff all the entries of $A(s)$ are constant?

score 63 · Answer 1 · 2026-03-26 13:30:13

63

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Why is $e^{\int_0^t A(s)} \mathrm{d} s$ a solution of $x' = Ax$ iff all the entries of $A(s)$ are constant?

Published on 26 Mar 2026 - 13:30

score 118 · Answer 2 · 2019-10-07 18:22:10

118

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Homework help: Exponential and Logarithmic Equations

Published on 07 Oct 2019 - 18:22

score 139 · Answer 3 · 2019-10-10 05:46:08

139

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At what rate do these common definitions converge to the constant $e=2.718...$?

Published on 10 Oct 2019 - 5:46

score 334 · Answer 4 · 2026-03-30 06:48:43

334

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How to rewrite $\lim_{h \to 0}\frac{e^h - 1}{h}=1$ into $\lim_{n \to +\infty}\left(\frac{x}{n}+1\right)^n=e^x$

Published on 30 Mar 2026 - 6:48

score 467 · Answer 5 · 2026-03-27 08:38:25

467

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Round-off error and exponential function

Published on 27 Mar 2026 - 8:38

score 308 · Answer 6 · 2019-10-11 08:40:30

308

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For what value of $k$ does $\exp(x)-k=\ln(x)$ have exactly one solution? Is there a closed form for this k?

Published on 11 Oct 2019 - 8:40

score 294 · Answer 7 · 2019-10-11 14:58:34

294

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Inequality : $\frac{a}{\exp(a+b)}+\frac{b}{\exp(b+c)}+\frac{c}{\exp(c+a)}\leq \exp\Big(\frac{-2}{3}\Big)$

Published on 11 Oct 2019 - 14:58

score 49 · Answer 8 · 2019-10-11 15:03:46

49

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Tricky exponentialccomposite function

Published on 11 Oct 2019 - 15:03

score 101 · Answer 9 · 2026-03-27 17:36:20

101

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Solving an exponential inequality $4^x + 25^x + 0.01^x \lt 2$ without using logarithms

Published on 27 Mar 2026 - 17:36

score 94 · Answer 10 · 2019-10-11 22:41:40

94

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Exponential Equation with different bases and a constant

Published on 11 Oct 2019 - 22:41

score 86 · Answer 11 · 2019-10-11 22:47:32

86

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Solve $5^{x/2}-2^x=1$

Published on 11 Oct 2019 - 22:47

score 102 · Answer 12 · 2026-04-01 16:25:18

102

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Find the number of real solutions of the equation $2^x+x^2=1$

Published on 01 Apr 2026 - 16:25

score 100 · Answer 13 · 2019-10-13 09:11:16

100

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Prove that if $\eta = \log(\frac{\phi}{1-\phi})$ then $\phi = \frac{1}{1+e^{-\eta}}$

Published on 13 Oct 2019 - 9:11

score 75 · Answer 14 · 2019-10-14 09:45:37

75

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exponential Radioactive decay

Published on 14 Oct 2019 - 9:45

score 49 · Answer 15 · 2019-10-14 11:22:28

49

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Exponent-like power series with coefficients of increasing complexity

Published on 14 Oct 2019 - 11:22

List Question

Why is $e^{\int_0^t A(s)} \mathrm{d} s$ a solution of $x' = Ax$ iff all the entries of $A(s)$ are constant?

Homework help: Exponential and Logarithmic Equations

At what rate do these common definitions converge to the constant $e=2.718...$?

How to rewrite $\lim_{h \to 0}\frac{e^h - 1}{h}=1$ into $\lim_{n \to +\infty}\left(\frac{x}{n}+1\right)^n=e^x$

Round-off error and exponential function

For what value of $k$ does $\exp(x)-k=\ln(x)$ have exactly one solution? Is there a closed form for this k?

Inequality : $\frac{a}{\exp(a+b)}+\frac{b}{\exp(b+c)}+\frac{c}{\exp(c+a)}\leq \exp\Big(\frac{-2}{3}\Big)$

Tricky exponentialccomposite function

Solving an exponential inequality $4^x + 25^x + 0.01^x \lt 2$ without using logarithms

Exponential Equation with different bases and a constant

Solve $5^{x/2}-2^x=1$

Find the number of real solutions of the equation $2^x+x^2=1$

Prove that if $\eta = \log(\frac{\phi}{1-\phi})$ then $\phi = \frac{1}{1+e^{-\eta}}$

exponential Radioactive decay

Exponent-like power series with coefficients of increasing complexity

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