Show that $\lim\limits_{(x,y)\to(0,0)}[x\sin(1/y) + y\sin(1/x)]$ exist
39148
Does $\lim_{(x,y)\to(0,0)}[x\sin (1/y)+y\sin (1/x)]$ exist?
5157
How to evaluate $ \lim_{(x,y)\to(0,0)}\frac{y^2\sin^2x}{x^4+y^4} $
13486
Show $\lim \limits_{n \to \infty} \frac{a_{n+1}}{a_n} = \|f\|_{\infty}$ for $f \in L^{\infty}$
6304
Evaluate $\lim_{(x,y) \to (0,0), x+y \neq 0}{\frac{\ln(1-x-y)}{x+y} } $
156011
Evaluate $\lim_{y\to 0} \dfrac {(x+y)\sec (x+y) - x\sec x}{y}$
110126
Prove that $\lim\limits_{(x,y) \to (0,0)} \frac{{x{y^2}}}{{{x^2} + {y^4}}} = 0$
31146
Does the limit $\lim_{(x,y)\to (0,0)} \frac {x^3y^2}{x^4+y^6}$ exist
138583
What is the limit of $\lim\limits_{x→∞}\frac{\sin x}{x}$
64628
Solving limits of a sine wave $\lim_{x\to+\infty}\frac{\sin(x)}{x}$
103055
Proving the quotient rule for limits
91278
The limit for $x\to 0$ of $x^3\sin (x)$ exists
150601
The limit of $\sin(1/x)$ as $x\to 0$ does not exists
9694
If $(y_{2n}-y_n) \to 0$ then $\lim_{n\to \infty} y_n$ exists
137963
Limit of $\frac{xy-z^2}{x^2+y^2+z^2}$ and $\frac{xy}{x^2+y^2}$ as $(x,y) \to (0,0)$
65266
A limit problem $\lim\limits_{x \to 0}\frac{x\sin(\sin x) - \sin^{2}x}{x^{6}}$
150917
Show that $\lim_{n\to \infty}\sin{n\pi x} =0$ if $x\in \mathbb{Z},$ but the limit fails to exist if $x\notin \mathbb{Z}.$
11516
Evaluate the limit: $\lim_{(x,y,z)\to(0,0,0)}\frac{xy+yz^2+xz^2}{x^2+y^2+z^4}$