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$f:\mathbb R \to \mathbb R$ is continuous and lim$_{n\to \infty} f(nx)=0$ for all real $x$ $\implies $ lim$_{x \to \infty}f(x)=0$

How to show square root of absolute of x, $\sqrt{|x|}$, is not Lipschitz continuous?

Dini's Theorem. Uniform convergence and Bolzano Weierstrass.

Let $f: \Bbb R \to [0,\infty)$ be a continuous function such that $g(x)=(f(x))^2$ is uniformly continuous. Which of the following is always true?

If $f(0) = 0$ and $|f'(x)|\leq |f(x)|$ for all $x\in\mathbb{R}$ then $f\equiv 0$ [duplicate]

Proof verification: the product of two continuous functions is continuous

Understand the mistake in solving the continuity problem

What does Structure-Preserving mean?

Why is $y=1/x$ a continuous function but not $y=(1/x)^2$?

Convergent sequences and choice [duplicate]

is the inverse of a absolutely continuous function with almost everywhere positive derivation absolutely continuous?

The proof that if f(x) is continuous at x=c, then 1/f(x) is continuous at x=c

Choose $3n$ points on a circle, show that there are two diametrically opposite point

A map between metric spaces preserving convergent sequences is continuous

Difficulty in finding a counterexample

Setting up / Troubleshooting Continuity-Camera

New posts in continuity

Chrome on Mac hands off to Safari on iPhone

Choice of $\delta$ for "brute force" proof of continuity of exponential function $e^x$

Help me correct my ideas of continuity

Countable-infinity-to-one function

$f:\mathbb R \to \mathbb R$ is continuous and lim$_{n\to \infty} f(nx)=0$ for all real $x$ $\implies $ lim$_{x \to \infty}f(x)=0$

How to show square root of absolute of x, $\sqrt{|x|}$, is not Lipschitz continuous?

Dini's Theorem. Uniform convergence and Bolzano Weierstrass.

Let $f: \Bbb R \to [0,\infty)$ be a continuous function such that $g(x)=(f(x))^2$ is uniformly continuous. Which of the following is always true?

If $f(0) = 0$ and $|f'(x)|\leq |f(x)|$ for all $x\in\mathbb{R}$ then $f\equiv 0$ [duplicate]

Proof verification: the product of two continuous functions is continuous

Understand the mistake in solving the continuity problem

What does Structure-Preserving mean?

Why is $y=1/x$ a continuous function but not $y=(1/x)^2$?

Convergent sequences and choice [duplicate]

is the inverse of a absolutely continuous function with almost everywhere positive derivation absolutely continuous?

The proof that if f(x) is continuous at x=c, then 1/f(x) is continuous at x=c

Choose $3n$ points on a circle, show that there are two diametrically opposite point

A map between metric spaces preserving convergent sequences is continuous

Difficulty in finding a counterexample

Setting up / Troubleshooting Continuity-Camera