# New post in Continuity

## Revisit "Prove that the inverse image of an open set is open"

January 17th, 2023

## Show that $f(x)=3x^{2}-2x+1$ is continuous at 2

August 16th, 2022

## Why is $f(x) = \sqrt{x}$ is continuous at $x=0$? Does $\lim_{x \to 0^{-}} \sqrt{x}$ exist?

August 16th, 2022

## Prove that a sum of continuous functions is continuous

October 23rd, 2022

## Find interval in which function is continuous.

October 30th, 2022

## Examples of unbounded continuous function $f:Q\cap[0,1]\rightarrow R$

September 17th, 2022

August 1st, 2022

August 1st, 2022

## How's g(x) = sin(x)/x removal discontinuity?

February 22nd, 2021

## Show $f$ is continuous at $(0,0)$ if $f(x,y) = \frac{x^3\sin(x+y) - y^4\ln(x^2+y^2)}{x^2+y^2}$ for $(x,y) \neq (0,0)$ and $f(0,0)=0$

January 24th, 2020

April 6th, 2020

## Use the definition of continuity to prove a function is defined at every nonnegative real number

October 29th, 2020

June 23rd, 2020

August 1st, 2022

## How to show map is non-singular

February 10th, 2020

August 1st, 2022

July 23rd, 2020

August 1st, 2022

## Proving continuity of composition of continuous functions

October 18th, 2020

## Apply the mean value theorem to find the largest possible value of $f(7)$

January 13th, 2020

May 11th, 2020

August 1st, 2022

## Show that the function $f$ is attain its minimum or maximum value and bounded on $\mathbb R$

January 14th, 2020

August 1st, 2022

August 1st, 2022

May 3rd, 2020

August 1st, 2022

August 1st, 2022

April 8th, 2020

August 1st, 2022