Is $\frac{\sin(x)}{x}$ continuous at $x=0$? Whats the value at $x=0$?
17029
How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
1331
Approximation of the Sine function near $0$
11387
Mean Value Theorem: $\frac{2}{\pi}<\frac{\sin x}{x}<1$
33499
For which $a\in \mathbb{R}$ is $f(x,y) = \frac{xy^a}{x^2+y^2}$ with $f(0,0)=0$ continuous?
26373
Uniform continuity of $f(x) = x \sin{\frac{1}{x}}$ for $x \neq 0$ and $f(0) = 0.$
88989
Why $x<\tan{x}$ while $0<x<\frac{\pi}{2}$?
23617
Determine whether $f(x)={\sin x \over x}$ is uniformly continuous in $\mathbb R$
19561
Why is $\frac{1}{\frac{1}{X}}=X$?
138583
What is the limit of $\lim\limits_{x→∞}\frac{\sin x}{x}$
123476
Prove $[\sin x]' = \cos x$ without using $\lim\limits_{x\to 0}\frac{\sin x}{x} = 1$
80488
Explanation of method for showing that $\frac{0}{0}$ is undefined
16375
Is the function differentiable at $0$?
141945
Why is $f(x) = \sqrt{x}$ is continuous at $x=0$? Does $\lim_{x \to 0^{-}} \sqrt{x}$ exist?
135565
Limit of $\frac{1}{x^2}-\frac{1}{\sin^2(x)}$ as $x$ approaches $0$
79299
Strange behavior of $\lim_{x\to0}\frac{\sin\left(x\sin\left(\frac1x\right)\right)}{x\sin\left(\frac1x\right)}$
83703
Show that $\int_{0}^{\infty}|\frac{\sin x}{x}|\,dx=\infty $
141273
When is $\sin(x)$ rational?