Question

Show that Let $f : \mathbb{R} \setminus \{0\} \to \mathbb{R}$ be defined by $f(x) = \frac{1}{x}$. Show $\lim_{x \to 0}\frac{1}{x}$ doesn't exist.

score 915 · Answer 1 · 2026-04-16 09:34:55

915

Views

Show that Let $f : \mathbb{R} \setminus \{0\} \to \mathbb{R}$ be defined by $f(x) = \frac{1}{x}$. Show $\lim_{x \to 0}\frac{1}{x}$ doesn't exist.

Published on 16 Apr 2026 - 9:34

score 140 · Answer 2 · 2026-04-09 03:40:21

140

Views

Interchanging limit and integral verification

Published on 09 Apr 2026 - 3:40

score 409 · Answer 3 · 2026-04-17 13:30:02

409

Views

$\lim_{(x,y)\to(1,2)} \left(\frac{\tan^{-1}x+\tan^{-1}\frac1y-\tan^{-1}3}{(x-1)(y-2)}\right)\sin^{-1}(y-2)$ using Polar Coordinates

Published on 17 Apr 2026 - 13:30

score 329 · Answer 4 · 2026-04-08 16:31:13

329

Views

Finding limit using Euler number

Published on 08 Apr 2026 - 16:31

score 132 · Answer 5 · 2026-04-16 21:52:22

132

Views

Calculating $\lim_{(x,y)\to(0,0)}f(x,y)$ where $f(x,y)= \begin{cases} \frac{e^x -e^y}{\log(x)-\log(y) } & \ x \neq y\\ xe^x & x=y \end{cases}$

Published on 16 Apr 2026 - 21:52

score 73 · Answer 6 · 2026-04-17 11:42:12

73

Views

$\lim_{\epsilon\rightarrow 0^{+}}{\int_{0}^{\infty}\,e^{-\epsilon x}\,\frac{|\sin{x}|^{t}} {x^{t-1}}\,dx}, \quad 1< t<2$

Published on 17 Apr 2026 - 11:42

score 59 · Answer 7 · 2026-04-16 11:23:29

$\lim_{n\to\infty}\int_{X}\lvert f_n -f \rvert \, d\mu=0$. Why does this imply that $\lim_{n\to\infty}\int_{X}f_n \, d\mu=\int_{X}f \, d\mu$?

score 993 · Answer 8 · 2026-04-09 01:30:25

993

Views

How is continuity of a constant function defined?

Published on 09 Apr 2026 - 1:30

score 49 · Answer 9 · 2026-04-16 13:00:01

49

Views

$f(x)= (x+y) \sin(\frac{1}{x}+ \frac{1}{y}), x\neq0, y\neq0$ Limit as $x\to0, y\neq0$

Published on 16 Apr 2026 - 13:00

score 2k · Answer 10 · 2026-05-10 23:14:11

2k

Views

Proof that every random variable has a median, proof check?

Published on 10 May 2026 - 23:14

score 309 · Answer 11 · 2026-05-11 06:34:23

309

Views

Dirac delta function as a product of Heaviside function and Exponent for large argument

Published on 11 May 2026 - 6:34

score 980 · Answer 12 · 2026-04-16 00:13:22

980

Views

Evaluate $\lim_{x \to 0+}{ (e^{1/\sin x}-e^{(1/x)})}$

Published on 16 Apr 2026 - 0:13

score 41 · Answer 13 · 2026-05-11 00:22:52

41

Views

Sequence of RV and Limits

Published on 11 May 2026 - 0:22

score 44 · Answer 14 · 2026-04-15 08:54:24

44

Views

Limit with a definite integral

Published on 15 Apr 2026 - 8:54

score 1.2k · Answer 15 · 2026-04-10 22:07:25

1.2k

Views

Limit of logarithm

Published on 10 Apr 2026 - 22:07

List Question

Show that Let $f : \mathbb{R} \setminus \{0\} \to \mathbb{R}$ be defined by $f(x) = \frac{1}{x}$. Show $\lim_{x \to 0}\frac{1}{x}$ doesn't exist.

Interchanging limit and integral verification

$\lim_{(x,y)\to(1,2)} \left(\frac{\tan^{-1}x+\tan^{-1}\frac1y-\tan^{-1}3}{(x-1)(y-2)}\right)\sin^{-1}(y-2)$ using Polar Coordinates

Finding limit using Euler number

Calculating $\lim_{(x,y)\to(0,0)}f(x,y)$ where $f(x,y)= \begin{cases} \frac{e^x -e^y}{\log(x)-\log(y) } & \ x \neq y\\ xe^x & x=y \end{cases}$

$\lim_{\epsilon\rightarrow 0^{+}}{\int_{0}^{\infty}\,e^{-\epsilon x}\,\frac{|\sin{x}|^{t}} {x^{t-1}}\,dx}, \quad 1< t<2$

$\lim_{n\to\infty}\int_{X}\lvert f_n -f \rvert \, d\mu=0$. Why does this imply that $\lim_{n\to\infty}\int_{X}f_n \, d\mu=\int_{X}f \, d\mu$?

How is continuity of a constant function defined?

$f(x)= (x+y) \sin(\frac{1}{x}+ \frac{1}{y}), x\neq0, y\neq0$ Limit as $x\to0, y\neq0$

Proof that every random variable has a median, proof check?

Dirac delta function as a product of Heaviside function and Exponent for large argument

Evaluate $\lim_{x \to 0+}{ (e^{1/\sin x}-e^{(1/x)})}$

Sequence of RV and Limits

Limit with a definite integral

Limit of logarithm

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