List questions from mean-value-theorem

Published on 12 Jul 2022 - 22:51

37

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Continuity and Differentiability of the Mean Value Function

Published on 16 Jul 2022 - 8:07

106

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Question regarding the limit of $f(x)= \sqrt{x+1} - \sqrt{x}$ using the MVT

Published on 25 Jul 2022 - 23:50

626

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Bounded gradient implies Lipschitz on non-convex set

Published on 03 Aug 2022 - 8:47

69

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Intuitive understanding for $f(x)=f'(x)$ in $(a,b)$ when $f(a)=f(b)=0$

Published on 07 Aug 2022 - 6:30

106

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The function $g : [a, b]\to\mathbb{R}$ is continuous on $[a, b]$, differentiable on $(a, b)$ and satisfies $g'(x) > 0$. Explain $g$ is injective.

Published on 09 Aug 2022 - 9:45

1.4k

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Prove that $0<\dfrac{1}{x}\ln(\dfrac{e^x-1}{x})<1$ for $x>0$

Published on 09 Aug 2022 - 17:28

54

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if $f(a) = f(b) = 0$ and $f(c)\neq0,$ then there exist $x_1 , x_2 \in \mathbb R $ s.t $f'(x_1) > 0$ and$ f'(x_2) <0$

Published on 20 Aug 2022 - 3:02

80

Views

A Limit of a Sum from an Integral

Published on 21 Aug 2022 - 6:55

65

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Inequality of a linearized function

Published on 21 Aug 2022 - 12:47

69

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In mean value theorem for integral of $f(x)$ on $[a,b]$, when can one ensures that $c\neq a$ and $c\neq b$

Published on 22 Aug 2022 - 15:57

127

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Relating the norm of a diffeomorphism to the distance in a Riemannian manifold

Published on 26 Aug 2022 - 13:28

178

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Prove that $\left|\int^{x+1}_x\sin(e^t)dt\right| \le \frac{2}{e^x}$

Published on 05 Sep 2022 - 20:14

65

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What will infinitesimals of derivative do with the mean value theorem?

Published on 09 Sep 2022 - 10:16

96

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Spivak, Ch. 20, Prob. *17a: Is the solution manual incorrect?

Published on 05 Oct 2022 - 3:13

List Question

Mean value theorem with measurability under convexity

Continuity and Differentiability of the Mean Value Function

Question regarding the limit of $f(x)= \sqrt{x+1} - \sqrt{x}$ using the MVT

Bounded gradient implies Lipschitz on non-convex set

Intuitive understanding for $f(x)=f'(x)$ in $(a,b)$ when $f(a)=f(b)=0$

The function $g : [a, b]\to\mathbb{R}$ is continuous on $[a, b]$, differentiable on $(a, b)$ and satisfies $g'(x) > 0$. Explain $g$ is injective.

Prove that $0<\dfrac{1}{x}\ln(\dfrac{e^x-1}{x})<1$ for $x>0$

if $f(a) = f(b) = 0$ and $f(c)\neq0,$ then there exist $x_1 , x_2 \in \mathbb R $ s.t $f'(x_1) > 0$ and$ f'(x_2) <0$

A Limit of a Sum from an Integral

Inequality of a linearized function

In mean value theorem for integral of $f(x)$ on $[a,b]$, when can one ensures that $c\neq a$ and $c\neq b$

Relating the norm of a diffeomorphism to the distance in a Riemannian manifold

Prove that $\left|\int^{x+1}_x\sin(e^t)dt\right| \le \frac{2}{e^x}$

What will infinitesimals of derivative do with the mean value theorem?

Spivak, Ch. 20, Prob. *17a: Is the solution manual incorrect?

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