prove the limit of $f(x,y)=\frac{x^3−y^3}{x^2−y^2}$ exists with an $\epsilon - \delta$ prove
32572
What is $\lim_{(x,y)\to(0,0)} \frac{(x^3+y^3)}{(x^2-y^2)}$?
6619
Prove that $\lim \limits_{(x,y,z) \to (0,0,0)} \frac{{xyz}}{{x+y+z}}=0$
105316
Prove : $|x - y| \leqslant \epsilon$ $\forall \epsilon > 0$ iff $x = y$
95962
proving a theorem from limit using Hopital rule
135700
Show that $\lim_{n \to \infty} (1/n)\sum_{i=1}^n f(x_i)$ exists
76249
Does the limit of function of two variables exist
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.$
98377
How can I prove this limit doesn't exist?
5402
Prove or the disprove the existence of a limit of integrals
63950
Prove that to each $\epsilon >0$, there exists a $\delta >0$ so that the Lebesgue integral...
62606
Non-existence of $\lim \limits_{(x, y) \to (0,0)} \frac{x^3 + y^3}{x - y} $
111205
Proving that $\lim_{k\to \infty}\frac{f(x_k)-f(y_k)}{x_k-y_k}=f'(c)$ where $\lim_{k\to \infty}x_k=\lim_{k\to \infty}y_k=c$ with $x_k<c<y_k$
128761
An $\varepsilon-\delta$ proof of $\lim_{x\rightarrow c} (2x^ 2 − 3x + 4) = 2c ^2 − 3c + 4$.
122762
Proving that the limit doesn't exist for $x$ other than $0$
91523
Prove this limit as $x\to\infty$
68830
How to prove that $\lim\limits_{\epsilon\rightarrow 0}\int_{-\infty}^{\infty}f_\epsilon(x)g(x)dx=g(0)$ (Dirac delta function))
153730
Show that $f(x)=x^2$ is continuous at $a=2$ using the $\delta-\epsilon$ definition of continuity.