To prove that the limit of a bi-variate function is nonexistent at a point
62606
Non-existence of $\lim \limits_{(x, y) \to (0,0)} \frac{x^3 + y^3}{x - y} $
69348
Prove that $\int \limits _{0}^{\infty}\frac{e^{-2x}-e^{-ax}}{x}\text{d}x$ converges for any $a>0$
37055
Show that $\lim _{r \to 0} \|T_rf−f\|_{L_p} =0.$
88259
prove that $\frac{1}{x}$ is not uniformly continuous on $(0,1)$
1474
How to prove limit of measurable functions is measurable
22598
When does the limit $\lim_{(x,y)\to(0,0)} \frac{x^ky^l}{x^{2p}+y^{2q}}$ exist?
77239
Limit point versus limit and implications for convergence
13249
Multivariable limit proof: $\lim\limits_{(x,y)\rightarrow (0,0)}\frac{\left|x\right|^a\left|y\right|^b}{\left|x\right|^c + \left|y\right|^d} = 0$
72960
How to prove this limit composition theorem?
70458
Show that it is possible that the limit $\displaystyle{\lim_{x \rightarrow +\infty} f'(x)} $ does not exist.
143227
Show that: $\lim \limits_{n\to\infty}\frac{x_n-x_{n-1}}{n}=0 $
85269
Proof that limit of (lnx)/x = 0 without LHopital
5402
Prove or the disprove the existence of a limit of integrals
104229
Show that $\lim\limits_{y\downarrow 0} y\mathbb{E}[\frac{1}{X};X>y]=0$.
28413
Limit of a continuous function
122769
Show that $\lim_{n\to \infty}\int_{[0,\infty]}\left(1+\dfrac{x}{n}\right)^n\exp(-ax)=\dfrac{1}{a-1}$
125667
Limit of a function of two variables