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Uniform-continuity
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Prove that sinx/x uniformly continuous at x [1; infinity) by using epsilon delta
August 1st, 2022
uniform-continuity
epsilon-delta
Show $f$ is continuous at $(0,0)$ if $f(x,y) = \frac{x^3\sin(x+y) - y^4\ln(x^2+y^2)}{x^2+y^2}$ for $(x,y) \neq (0,0)$ and $f(0,0)=0$
January 24th, 2020
continuity
multivariable-calculus
uniform-continuity
limits
Example of a continuous function which is not uniformly continuous at a given interval.
December 6th, 2020
uniform-continuity
real-analysis
continuity
Prove that the function $f(z) = \frac{1}{1-z}$ is not uniformly continuous on $(-1,1)$
February 8th, 2020
complex-numbers
uniform-continuity
epsilon-delta
Showing $\tan x$ is uniformly continuous in $[0,\pi/4]$
March 14th, 2020
uniform-continuity
Uniform continuity of functions of a complex variable
February 22nd, 2020
continuity
complex-analysis
uniform-continuity
Proving $\frac{1}{ x^2}$ is not uniformly continuous on $(0,2]$
August 1st, 2022
real-analysis
uniform-continuity
proof-writing
f(x)=cos(x^2) is not uniformly continuous
August 1st, 2022
uniform-continuity
An MCQ question on continuity.
December 13th, 2020
real-analysis
continuity
uniform-continuity
Prove $f_n (x) := n \sin (\frac{x}{n})$ is equicontinuous
August 1st, 2022
analysis
uniform-continuity
sequences-and-series
Tips for proving a $f(x)$ is not uniformly continuous
August 1st, 2022
real-analysis
uniform-continuity
Prove directly from definition that $\tan(x)$ is not uniformly continuous on $(-\pi/2, \pi/2)$
August 1st, 2022
uniform-continuity
general-topology
calculus
Compact Space: Locally Continuous $\implies$ Uniformly Continuous
June 11th, 2020
uniform-continuity
continuity
metric-spaces
general-topology
compactness
Prove that $f(x)=x\sin(x)$ is not a uniformly continuous function
August 1st, 2022
uniform-continuity
real-analysis
Show that the cumulative distribution function is uniformly continuous.
September 27th, 2020
functional-analysis
functions
uniform-continuity
Hölder continuous functions are uniformly continuous
April 24th, 2020
real-analysis
proof-verification
proof-writing
uniform-continuity
holder-spaces
Uniform continuity of continuous periodic function
August 1st, 2022
real-analysis
uniform-continuity
Proving uniform continuity of absolute value
April 14th, 2020
absolute-value
real-analysis
analysis
uniform-continuity
Proving $1\over x^2$ is not uniformly continuous
February 10th, 2020
real-analysis
uniform-continuity
Proving that the exponential function is not uniformly continuous
March 7th, 2020
real-analysis
uniform-continuity
epsilon-delta
exponential-function
proof-verification
Prove that a monotonic bounded function is uniformly continuous
January 14th, 2020
uniform-continuity
continuity
real-analysis
Is $f(x)=\frac{1}{x^2+1}$ uniformly continuous on $\mathbb{R}$?
August 1st, 2022
continuity
epsilon-delta
uniform-continuity
calculus
real-analysis
Prove that if $f$ and $g$ are uniformly continuous on A and are both bounded on A, then $fg$ is uniformly continuous on A.
March 28th, 2020
continuity
epsilon-delta
uniform-continuity
real-analysis
continuous bounded function on the bounded open interval ]a,b[ that is not uniformly continuous on ]a,b[
August 19th, 2020
real-analysis
uniform-continuity
How to show that "Uniformly continuous implies continuous"?
February 5th, 2020
proof-writing
real-analysis
uniform-continuity
continuity
Prove that $\ln x$ is not uniformly continuous on $(0,1]$
February 6th, 2020
real-analysis
calculus
uniform-continuity
continuity
If a sequence $(f_n)$ do not converge uniformly, then no subsequence of $(f_n)$ converge uniformly
March 5th, 2020
sequences-and-series
uniform-continuity
functional-analysis
uniform-convergence
real-analysis
two functions are uniformly continuous on some interval I and each is bounded on I then their product is also uniformly continuous on I .
August 19th, 2020
uniform-continuity
$f(x)$ is continuous on $(a,b)$ such that $f(a)f(b) < 0$. Show the existence of $c$ element of $(a,b)$ such that $f(c) = 0$
August 1st, 2022
continuity
real-analysis
calculus
uniform-continuity
Is $\cos\sqrt{xy}$ uniformly continuous?
August 1st, 2022
real-analysis
continuity
uniform-continuity
multivariable-calculus
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