query: Showing that a function is continuous for $x$
positive_passages.docid: 149354
positive_passages.text: Proof of continuity $f(x+y) = f(x) + f(y)$
negative_passages.docid: 109896
negative_passages.text: Proving that the function $f(x,y)=\frac{x^2y}{x^2 + y^2}$ with $f(0,0)=0$ is continuous at $(0,0)$.
negative_passages.docid: 110458
negative_passages.text: Show that if $f$ is continuous on $(0,1)$ and $\lim_{x \to 0}f(x) = + \infty$ then $f$ is not uniformly continuous
negative_passages.docid: 17223
negative_passages.text: Continuity of an inverse function.
negative_passages.docid: 125682
negative_passages.text: Proof verification: the product of two continuous functions is continuous
negative_passages.docid: 151410
negative_passages.text: Inequality of continuous functions
negative_passages.docid: 97256
negative_passages.text: For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
negative_passages.docid: 131992
negative_passages.text: A problem on continuous functions
negative_passages.docid: 23294
negative_passages.text: Show that the function $f = \frac{xy}{x^2 + y^2}$ is continuous along every horizontal and every vertical line
negative_passages.docid: 15579
negative_passages.text: Show that $f$ is uniformly continuous if limit exists
negative_passages.docid: 53497
negative_passages.text: Prove that the function is continuous and differentiable (not as easy as it sounds imo)
negative_passages.docid: 75479
negative_passages.text: Proving that this function is continuous on $G\times G$
negative_passages.docid: 15727
negative_passages.text: show that if $f$ is uniformly differentiable then prove that $f'$ is continuous
negative_passages.docid: 134752
negative_passages.text: Proof (epsilon delta) for the continuity of a function at a point
negative_passages.docid: 130299
negative_passages.text: Prove that if a function $f: X\to Y$ continuous then its graph is closed
negative_passages.docid: 98772
negative_passages.text: Continuity of a function in $\mathbb{R}$
negative_passages.docid: 87239
negative_passages.text: Prove functions defined by sup and inf are continuous