Prove that $\lim_{x \to \frac{2}{\pi}}\lfloor \sin \frac{1}{x} \rfloor=0$ in the $\epsilon$-$\delta$ way
45728
Proving a limit of a trigonometric function: $\lim_{x \to 2/\pi}\lfloor \sin \frac{1}{x} \rfloor=0$
110126
Prove that $\lim\limits_{(x,y) \to (0,0)} \frac{{x{y^2}}}{{{x^2} + {y^4}}} = 0$
122769
Show that $\lim_{n\to \infty}\int_{[0,\infty]}\left(1+\dfrac{x}{n}\right)^n\exp(-ax)=\dfrac{1}{a-1}$
74684
$\lim_{x \to 0} {1-x\cot x\over x^2}$
112595
Prove that the limit of this sequence is $\frac{1}{2}(1 + \sqrt{5})$
100387
Using $\epsilon-\delta$ to prove that a limit is not a specific number
135359
How to prove that limit doesn't exist using epsilon-delta definition?
30181
Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
6619
Prove that $\lim \limits_{(x,y,z) \to (0,0,0)} \frac{{xyz}}{{x+y+z}}=0$
132873
Understanding Epsilon-Delta Proof
129042
Prove that $\lim_{a \to 0^{+}} \int_{0}^{a} \frac{1}{\sqrt{\cos(x)-\cos(a)}} \;dx=\frac{\pi}{\sqrt{2}}$
5529
Proving that $x$ is irrational if $x-\lfloor x \rfloor + \frac1x - \left\lfloor \frac1x \right\rfloor = 1$
155377
How can I calculate this limit: $\lim\limits_{x\to 0} x\left\lfloor\frac{1}{x}\right\rfloor$?
45480
Does $\sum\frac{(-1)^{\lfloor \sqrt n\rfloor}}{ n}$ converge?
108917
Use $\delta-\epsilon$ to show that $\lim_{n\to\infty} a^{\frac{1}{n}} = 1$?
156478
Prove that $\lim_{n\rightarrow\infty}\frac{x_1^2+x_2^2+\cdots+x_n^2}{n^2}=0$
17019
Show that: $\lim\limits_{r\to\infty}\int\limits_{0}^{\pi/2}e^{-r\sin \theta}\text d\theta=0$