Why is $\lim_{(x_1,x_2) \to (0,0)}\frac{x_1x_2}{x_1^2 + x_2^2} ≠ 0$
109994
Show discontinuity of $\frac{xy}{x^2+y^2}$
135565
Limit of $\frac{1}{x^2}-\frac{1}{\sin^2(x)}$ as $x$ approaches $0$
74684
$\lim_{x \to 0} {1-x\cot x\over x^2}$
4289
$\lim_{x\to0}\dfrac{1}{x}-\lim_{x\to0}\dfrac{1}{x}$
60831
Need hint for $\lim_{x\to 0} \frac{(x+1)^\frac{1}{x}-e}{x}$
11516
Evaluate the limit: $\lim_{(x,y,z)\to(0,0,0)}\frac{xy+yz^2+xz^2}{x^2+y^2+z^4}$
158447
Limit as $(x,y)$ approaches $(0,0)$ of $(1+x^2+y^2)^{\frac{1}{x^2+y^2+xy^2}}$
123436
Precise definition of limits and $\lim_{x\to-1}\frac1{\sqrt{x^2+3}}=\frac12$
6619
Prove that $\lim \limits_{(x,y,z) \to (0,0,0)} \frac{{xyz}}{{x+y+z}}=0$
30181
Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
80440
Limit of $(x_n)$ with $0<x_1<1$ and $x_{n + 1} = x_n - x_n^{n + 1}$
90398
How to show $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$?
12375
Prove $\lim_{(x,y) \to (0,0)} \frac{x^3y}{x^4+y^2} = 0$
53109
Why is this limit $\lim_{n \to \infty}(1 + \frac{1}{n})^n$ equal to $e$?
11382
Limit $\lim\limits_{x\to0}\frac1{\ln(x+1)}-\frac1x$
98392
Value of the limit $\lim_{x \to 0} \frac{\sin(\frac{1}{x})}{\sin(\frac{1}{x})}$
43852
Evaluate $\lim_{x\to 0}\frac{e^{(x+1)^{1/x}}-(x+1)^{e/x}}{x^2}$