periodic functions, proof that lim x → + ∞ sin(x) does not exist
43547
If a function is convergent and periodic, then it is the constant function.
19056
Find the limit of $(2\sin x-\sin 2x)/(x-\sin x)$ as $x\to 0$ without L'Hôpital's rule
133874
Proof that $\lim_{n\to\infty}{\sin{100n}}$ does not exist
65266
A limit problem $\lim\limits_{x \to 0}\frac{x\sin(\sin x) - \sin^{2}x}{x^{6}}$
135359
How to prove that limit doesn't exist using epsilon-delta definition?
150601
The limit of $\sin(1/x)$ as $x\to 0$ does not exists
12446
integral involving a periodic function
86458
Choosing $2$ paths through $(0,0)$ to show: $ \lim_{(x,y) \to (0,0)}\frac{xy^2}{x^2 + y^4}$ does not exist
157731
Show that one-sided limits always exist for a monotone function (on an interval)
6465
How to prove periodicity of $\sin(x)$ or $\cos(x)$ starting from the Taylor series expansion?
37812
Prove that the function$\ f(x)=\sin(x^2)$ is not uniformly continuous on the domain $\mathbb{R}$.
46642
Continuity of $\sin(x)/x$
33486
Negation of the Definition of Limit of a Function
101546
Lebesgue integral $\int_{(0, \infty)} \frac{\sin x}{x} dm$ doesn't exist but improper Riemann integral exists
129697
Prove that a limit doesn't exist
80720
What paths to choose to prove that $\lim_{(x,y) \to (0,0)}\frac{xy^2}{x^2 - y^2}$ does not exist?
91278
The limit for $x\to 0$ of $x^3\sin (x)$ exists