Question

Show that $f(x,y) = (e^x\cos y, e^x \sin y)$ is one to one on $E := \{(x,y):x \in \mathbb{R} ,0 < y < \frac{\pi}{2} \}$.

score 52 · Answer 1 · 2020-03-05 23:18:30

52

Views

Show that $f(x,y) = (e^x\cos y, e^x \sin y)$ is one to one on $E := \{(x,y):x \in \mathbb{R} ,0 < y < \frac{\pi}{2} \}$.

Published on 05 Mar 2020 - 23:18

score 136 · Answer 2 · 2020-03-06 06:50:12

Solutions to inverse trig equation $\tan^{-1}\left(\frac{2x}{1-x^2}\right)+\cot^{-1}\left(\frac{1-x^2}{2x}\right)=\frac{2\pi}{3}$

score 67 · Answer 3 · 2026-03-30 10:13:28

67

Views

Finding the Inverse of the Product of Two Gamma Functions

Published on 30 Mar 2026 - 10:13

score 44 · Answer 4 · 2026-03-28 14:37:52

44

Views

Are all symmetrical real matrices invertible (except $A = 0$)?

Published on 28 Mar 2026 - 14:37

score 304 · Answer 5 · 2020-03-09 17:54:11

304

Views

Matrices of right and left eigenvectors ($\mathbb{R}$ and $\mathbb{L}$): proof that $\mathbb{L}\mathbb{R} = \mathbb{I}$

Published on 09 Mar 2020 - 17:54

score 2.4k · Answer 6 · 2020-03-09 21:01:53

2.4k

Views

Difficulty understanding the inverse of a homogeneous transformation matrix

Published on 09 Mar 2020 - 21:01

score 42 · Answer 7 · 2026-03-26 06:21:04

42

Views

How to reverse the bend in a 2 DOF arm using inverse kinematics

Published on 26 Mar 2026 - 6:21

score 359 · Answer 8 · 2020-03-12 05:01:29

359

Views

Calculus 2: Inverse Trig Functions

Published on 12 Mar 2020 - 5:01

score 47 · Answer 9 · 2026-03-28 22:08:21

47

Views

derive an equation from an equation with $\log$ and $\tan$

Published on 28 Mar 2026 - 22:08

score 629 · Answer 10 · 2020-03-12 10:36:50

629

Views

Inverse Laplace Transform for $ \frac{1}{p} \cdot \frac{1}{\sqrt{p + b}}\cdot e^{-x \sqrt{p+b}} $

Published on 12 Mar 2020 - 10:36

score 2k · Answer 11 · 2020-03-13 08:16:41

2k

Views

Find the inverse function of $y=x^2-2x$ where $x\gt 1$

Published on 13 Mar 2020 - 8:16

score 80 · Answer 12 · 2020-03-13 23:08:16

80

Views

$f(x^{-1})$ = $\left(f(x)\right)^{-1}$. Does this property have a name?

Published on 13 Mar 2020 - 23:08

score 105 · Answer 13 · 2026-03-25 23:42:16

105

Views

Assuming $A = Df(x_0)$ is invertible, prove that there exists $\mu > 0$ such that for all $x \in R^n$ $ ||Ax|| \geq \mu||x||$

Published on 25 Mar 2026 - 23:42

score 153 · Answer 14 · 2026-03-28 16:44:19

153

Views

Why sometimes the trace of a inverse matrix is very high and sometimes is low?

Published on 28 Mar 2026 - 16:44

score 112 · Answer 15 · 2026-03-25 12:46:32

112

Views

Area between two functions is the same as area between the inverse functions

Published on 25 Mar 2026 - 12:46

List Question

Show that $f(x,y) = (e^x\cos y, e^x \sin y)$ is one to one on $E := \{(x,y):x \in \mathbb{R} ,0 < y < \frac{\pi}{2} \}$.

Solutions to inverse trig equation $\tan^{-1}\left(\frac{2x}{1-x^2}\right)+\cot^{-1}\left(\frac{1-x^2}{2x}\right)=\frac{2\pi}{3}$

Finding the Inverse of the Product of Two Gamma Functions

Are all symmetrical real matrices invertible (except $A = 0$)?

Matrices of right and left eigenvectors ($\mathbb{R}$ and $\mathbb{L}$): proof that $\mathbb{L}\mathbb{R} = \mathbb{I}$

Difficulty understanding the inverse of a homogeneous transformation matrix

How to reverse the bend in a 2 DOF arm using inverse kinematics

Calculus 2: Inverse Trig Functions

derive an equation from an equation with $\log$ and $\tan$

Inverse Laplace Transform for $ \frac{1}{p} \cdot \frac{1}{\sqrt{p + b}}\cdot e^{-x \sqrt{p+b}} $

Find the inverse function of $y=x^2-2x$ where $x\gt 1$

$f(x^{-1})$ = $\left(f(x)\right)^{-1}$. Does this property have a name?

Assuming $A = Df(x_0)$ is invertible, prove that there exists $\mu > 0$ such that for all $x \in R^n$ $ ||Ax|| \geq \mu||x||$

Why sometimes the trace of a inverse matrix is very high and sometimes is low?

Area between two functions is the same as area between the inverse functions

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