List questions from inverse-function

971

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Any epsilon-delta proof of the continuity of the inverse of a real-valued strictly monotonic continuous function on an open interval?

Published on 10 May 2026 - 17:02

50

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Values of Inverse Trigonometic Functions without a Calculator

Published on 12 Apr 2026 - 4:04

1.9k

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Range of $ f(x)=\ln(x+\sqrt{x^2+1}) $

Published on 10 May 2026 - 15:02

776

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Find a left-inverse for the function $f:\Bbb Z \to \Bbb Z$ given by $f(n)=2n+1$.

Published on 15 Apr 2026 - 4:18

297

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Sigmoid functions for a biased random number generator

Published on 13 Apr 2026 - 4:41

305

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Integrate $\sin^{-1}\frac{2x}{1+x^2}$

Published on 15 Apr 2026 - 23:32

99

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Integral of the form $\int_a^b f^{-1}(x)\,dx$

Published on 17 Apr 2026 - 6:54

71

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Derivate of a inverse function

Published on 15 Apr 2026 - 20:44

49

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Smoothness of $f^{-1}$ at $f(0)$ from asymptotics of $f:[0,\infty)\to \mathbb{R}$

Published on 16 Apr 2026 - 13:53

1k

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A formula for higher order derivatives of inverse function

Published on 11 Apr 2026 - 2:38

392

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Find $\int\arcsin(\sqrt{x})dx$

Published on 16 Apr 2026 - 4:31

267

Views

Integrate $\int\tan^{-1}\sqrt{\frac{1-x}{1+x}}dx$

Published on 17 Apr 2026 - 9:27

305

Views

Integrate $\int \frac{dx}{\sqrt{(x-a)(b-x)}}$

Published on 16 Apr 2026 - 13:15

60

Views

Find x from the given relation

Published on 16 Apr 2026 - 1:26

291

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Find derivative of arcsec 2t

Published on 16 Apr 2026 - 8:29

List Question

Any epsilon-delta proof of the continuity of the inverse of a real-valued strictly monotonic continuous function on an open interval?

Values of Inverse Trigonometic Functions without a Calculator

Range of $ f(x)=\ln(x+\sqrt{x^2+1}) $

Find a left-inverse for the function $f:\Bbb Z \to \Bbb Z$ given by $f(n)=2n+1$.

Sigmoid functions for a biased random number generator

Integrate $\sin^{-1}\frac{2x}{1+x^2}$

Integral of the form $\int_a^b f^{-1}(x)\,dx$

Derivate of a inverse function

Smoothness of $f^{-1}$ at $f(0)$ from asymptotics of $f:[0,\infty)\to \mathbb{R}$

A formula for higher order derivatives of inverse function

Find $\int\arcsin(\sqrt{x})dx$

Integrate $\int\tan^{-1}\sqrt{\frac{1-x}{1+x}}dx$

Integrate $\int \frac{dx}{\sqrt{(x-a)(b-x)}}$

Find x from the given relation

Find derivative of arcsec 2t

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