Is the function $\frac{\sin{x}}{x}$ continuous at $x=0$?
46642
Continuity of $\sin(x)/x$
72278
What is the value of $\frac{\sin x}x$ at $x=0$?
152105
When is $x^{\alpha}\sin(x^{\beta})$ uniformly continuous for $\alpha, \beta > 0$?
17029
How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
86860
Continuity of differentiable function $x^2\sin(1/x)$
118628
Is the function $f(x)=|x|^{1/2}$ Lipschitz continuous?
155170
Proving $\sin(x^2)$ Continuous but Not Uniformly Continuous with non-standard Definition
77322
Uniform continuity of $\sin(x\sin x )$ for all $x\in (0,\infty)$
120707
Proof regard to the function $ f\left(x\right)=\begin{cases} x^{2}\sin\left(\frac{1}{x^{2}}\right) & x\neq0\\ 0 & x=0 \end{cases} $
150601
The limit of $\sin(1/x)$ as $x\to 0$ does not exists
112898
Derivative of sin(x)/x at $0$ by definition of derivative
99105
Are the functions $\sin^n(x)$ linearly independent?
125088
show that $ \lim(\sin(\frac{1}{x}))$ as $x$ approaches zero does not exist.
121848
If $f(x)=\begin {cases} x^a\sin (1/x) & x\not =0 \\ 0 & x =0 \end {cases}$ is continuous but not differentiable at $x=0$ find $a$
138583
What is the limit of $\lim\limits_{x→∞}\frac{\sin x}{x}$
150235
$\epsilon$-$\delta$ proof that $f(x) = x \sin(1/x)$, $x \ne 0$, is continuous
141423
The continuity of $f(x,y) = \frac {\sin (xy)} {\sqrt {x^2 + y^2}}$ at $(0,0)$