List questions from mean-value-theorem

Published on 13 Feb 2024 - 23:44

75

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Existence of $1/(e-1)$ value of a continous and differentiable function $f:[0,1]\to \mathbb R$ given $f(1)=1, f(0)=0$

Published on 22 Feb 2024 - 3:59

62

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Limit of a sequence of the real root of a family of polynomials

Published on 24 Feb 2024 - 6:02

25

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Mean value theorem for second derivative, Zorich

Published on 26 Feb 2024 - 11:57

34

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Showing that $f$ is the zero map by applying the mean value theorem

Published on 07 Mar 2024 - 11:28

36

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How does the mean value theorem with Hölder seminorms depend on dimension?

Published on 08 Mar 2024 - 21:26

110

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Prove that $\lim_{x\rightarrow\infty}f(2x)-f(x)=0$ using the Mean value theorem

Published on 09 Mar 2024 - 21:44

98

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What is the Second mean value theorem for integrals?

Published on 12 Mar 2024 - 14:12

35

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$\alpha$-Hölder function with $\alpha > 1$ is constant.

Published on 17 Mar 2024 - 2:15

141

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Multidimensional Mean Value Theorem with arbitrary norm

Published on 17 Mar 2024 - 9:24

51

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Mean value theorem $f'(a)=f'(b)$

Published on 17 Mar 2024 - 13:24

64

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How can I evaluate the limit of $\theta$ in the expression $f(x+h)-f(x)=h f'(x+\theta h)$?

Published on 25 Mar 2024 - 15:22

84

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Prove by Mean Value Theorem: $\frac15(b-a) < \arctan\left(1+\frac1a\right) - \arctan\left(1+\frac1a\right)$

Published on 17 Mar 2015 - 19:10

49

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Mean value theorem question - proving F constant - answer check

Published on 20 Feb 2022 - 16:14

44

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Use mathematical induction to show that eˣ > 1 + ⁿ∑ᵣ xʳ/r!

Published on 21 Feb 2022 - 19:35

List Question

Question about theorem 9.21 in Rudin's PMA

Existence of $1/(e-1)$ value of a continous and differentiable function $f:[0,1]\to \mathbb R$ given $f(1)=1, f(0)=0$

Limit of a sequence of the real root of a family of polynomials

Mean value theorem for second derivative, Zorich

Showing that $f$ is the zero map by applying the mean value theorem

How does the mean value theorem with Hölder seminorms depend on dimension?

Prove that $\lim_{x\rightarrow\infty}f(2x)-f(x)=0$ using the Mean value theorem

What is the Second mean value theorem for integrals?

$\alpha$-Hölder function with $\alpha > 1$ is constant.

Multidimensional Mean Value Theorem with arbitrary norm

Mean value theorem $f'(a)=f'(b)$

How can I evaluate the limit of $\theta$ in the expression $f(x+h)-f(x)=h f'(x+\theta h)$?

Prove by Mean Value Theorem: $\frac15(b-a) < \arctan\left(1+\frac1a\right) - \arctan\left(1+\frac1a\right)$

Mean value theorem question - proving F constant - answer check

Use mathematical induction to show that eˣ > 1 + ⁿ∑ᵣ xʳ/r!

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