If $f(x) =\left(\frac{2x^4y-5x^2y^2+y^5}{(x^2+y^2)^2}\right)$, how to choose $\delta$ so that $\sqrt{x^2+y^2}<\delta\implies |f(x,y)|<0.01\,$?
6238
How to find delta, for a given epsilon?
40463
Evaluating $\lim _{x\to 1}\left(\frac{\sqrt[3]{x}-1}{2\sqrt{x}-2}\right)$
139215
Find the value of $\lim_{x \to - \infty} \left( \sqrt{x^2 + 2x} - \sqrt{x^2 - 2x} \right)$
61162
Show that $\left(\int_0^1 f(x)\,dx\right)^2\leq2\int_0^1x\, f(x)^2\,dx $
10749
Proving $\lim_{x\to 1} x^3=1$ with $\epsilon$-$\delta$ definition
146640
Computing $\lim_{(x,y)\to (0,0)}\frac{x+y}{\sqrt{x^2+y^2}}$
145368
How to show $f:Y\to X^{+}$ is continuous?
59518
MLE of $\delta$ for the distribution $f(x)=e^{\delta-x}$ for $x\geq\delta$.
135092
How exactly can't $\delta$ depend on $x$ in the definition of uniform continuity?
141945
Why is $f(x) = \sqrt{x}$ is continuous at $x=0$? Does $\lim_{x \to 0^{-}} \sqrt{x}$ exist?
141423
The continuity of $f(x,y) = \frac {\sin (xy)} {\sqrt {x^2 + y^2}}$ at $(0,0)$
21954
A question about $f(x)\equiv 0$
139974
how to find epsilon-delta definition of a limit
89429
Prove $\sup \left| f'\left( x\right) \right| ^{2}\leqslant 4\sup \left| f\left( x\right) \right| \sup \left| f''\left( x\right) \right| $
76990
Find $\lim_{x \to - \infty} \left(\frac{4^{x+2}- 2\cdot3^{-x}}{4^{-x}+2\cdot3^{x+1}}\right)$
28088
When is $f_{xy}(x,y)\neq f_{yx}(x,y)?$
108917
Use $\delta-\epsilon$ to show that $\lim_{n\to\infty} a^{\frac{1}{n}} = 1$?