show $\lim\limits_{(x,y)\to(0,0)}\frac{|x|^a|y|^b}{|x|^c+|y|^d}$ exists and equals $0$?
37489
Show that $ \lim_{(x,y) \to 0} \frac {|x|^ \alpha |y|^ \beta} {|x|^ \gamma + |y|^ \delta} \text {exists} \iff \alpha/\gamma + \beta/\delta > 1.$
64169
Why isn't $\lim \limits_{x\to\infty}\left(1+\frac{1}{x}\right)^{x}$ equal to $1$?
67853
Prove existence of $\lim_{(x,y) \rightarrow (0,2)} \frac{x (y-2)^3}{3x - 5(y-2)^4}$
104229
Show that $\lim\limits_{y\downarrow 0} y\mathbb{E}[\frac{1}{X};X>y]=0$.
51212
How do I solve $\lim\limits_{x\to\infty} \ \frac{\ln \ x}{x} = 0$?
92685
Let $f:[0,1]\to\mathbb{R}$ be a continuous function. Calculate $\lim\limits_{c\to 0^+} \int_{ca}^{cb}\frac{f(x)}{x}\,dx$
90377
Proving the general limit $\lim_{n\to\infty} \frac{an+c}{bn+d} = \frac{a}{b}$
151329
Showing $\lim_{(x,y) \to (0,0)} \sin (xy) / xy = 1$
85412
Epsilon delta proof for $\lim_\limits{x\to a} \sqrt{x} = \sqrt{a}$ where $a>0$
125860
Showing that $\lim\limits_{n\to\infty}x_n$ exists, where $x_{n} = \sqrt{1 + \sqrt{2 + \sqrt{3 + ...+\sqrt{n}}}}$
126578
Evaluate $\lim_{(x,y)\to(0,0)}\frac{\cos(xy)-1}{x^2y^2}$
32572
What is $\lim_{(x,y)\to(0,0)} \frac{(x^3+y^3)}{(x^2-y^2)}$?
136024
Show that the limit does not exist $\lim_{(x, y) \to (0,0)}\frac{5x^2}{x^2 + y^2}$
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
30834
limit of $\lim\limits_{x \to \infty}((x+1)^a - x^a)$
132747
How can one show that $ f(0)\ln(\frac{b}{a})=\lim_{\epsilon\rightarrow 0}\int_{\epsilon a}^{\epsilon b} \frac{f(x)}{x}dx$?
120777
How to formally prove that if $\lim \limits_{n \to \infty}a_n=\infty$, then $\lim \limits_{n \to \infty}\frac{1}{a_n}=0$.