query: Use epsilon-delta definition to show $f(x)=x^2$ is continuous
positive_passages.docid: 153730
positive_passages.text: Show that $f(x)=x^2$ is continuous at $a=2$ using the $\delta-\epsilon$ definition of continuity.
negative_passages.docid: 135534
negative_passages.text: Prove that $\lim_{x\to 2}x^2=4$ using $\epsilon-\delta$ definition.
negative_passages.docid: 130023
negative_passages.text: Prove that the sum of two continuous functions is continuous
negative_passages.docid: 115077
negative_passages.text: Prove continuity for cubic root using epsilon-delta
negative_passages.docid: 28399
negative_passages.text: Showing $f$ is constant
negative_passages.docid: 135092
negative_passages.text: How exactly can't $\delta$ depend on $x$ in the definition of uniform continuity?
negative_passages.docid: 58664
negative_passages.text: Proving a function is continuous for a fixed variable
negative_passages.docid: 46834
negative_passages.text: show that a distance function is continuous
negative_passages.docid: 127538
negative_passages.text: Show $f(x)=x\ln x$ is not uniformly continuous
negative_passages.docid: 50103
negative_passages.text: Show that a continuous function satisfying $f(2^x)=f(3^x)$ for $x\in (0,\infty)$ is a constant function
negative_passages.docid: 34940
negative_passages.text: Continuity of $f(x) = x^n$
negative_passages.docid: 127449
negative_passages.text: Uniform continuous of $f(x,y) = \sin(x^2+y)$
negative_passages.docid: 9918
negative_passages.text: Please verify my epsilon - delta proof $\lim_{x\to 2}⁡(x^3 )=8,$ and $0 < x < 4$
negative_passages.docid: 139744
negative_passages.text: For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
negative_passages.docid: 38885
negative_passages.text: Prove the function is continuous, exercise from Conway's "Functions of One Complex Variable I"
negative_passages.docid: 145163
negative_passages.text: How do I show a function on 2-adic units is continuous?
negative_passages.docid: 20273
negative_passages.text: Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.