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Continuity
New post in Continuity
Revisit "Prove that the inverse image of an open set is open"
January 17th, 2023
real-analysis
general-topology
continuity
Show that $f(x)=3x^{2}-2x+1$ is continuous at 2
August 16th, 2022
proof-verification
real-analysis
continuity
Why is $f(x) = \sqrt{x}$ is continuous at $x=0$? Does $\lim_{x \to 0^{-}} \sqrt{x}$ exist?
August 16th, 2022
continuity
limits
calculus
Prove that a sum of continuous functions is continuous
October 23rd, 2022
continuity
sequences-and-series
Find interval in which function is continuous.
October 30th, 2022
continuity
Examples of unbounded continuous function $f:Q\cap[0,1]\rightarrow R$
September 17th, 2022
continuity
Find the points of discontinuity of $ f(x) =\frac{e^x-1}{\log_{e}(1+2x)}$ if $x\ne0$ and $f(0)=7$
August 1st, 2022
real-analysis
continuity
Use continuity to evaluate the limit.
August 1st, 2022
calculus
continuity
trigonometry
How's g(x) = sin(x)/x removal discontinuity?
February 22nd, 2021
calculus
continuity
limits
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
uniform-continuity
limits
multivariable-calculus
Choose constants a and b so that the function is continuous everywhere!
April 6th, 2020
continuity
limits
Use the definition of continuity to prove a function is defined at every nonnegative real number
October 29th, 2020
continuity
real-analysis
How to find the average value of a discontinuous function
June 23rd, 2020
continuity
average
Finding the maxima without second derivative test
August 1st, 2022
calculus
functions
optimization
continuity
How to show map is non-singular
February 10th, 2020
multivariable-calculus
real-analysis
vector-spaces
continuity
The points where function is discontinuous,are those points counted/considered in the domain of the function.
August 1st, 2022
continuity
real-analysis
functions
How to find E(x) and Var(x) in this specific continuous probability distribution.
July 23rd, 2020
expectation
probability
probability-distributions
continuity
How to use graph to determine where f(x) > 0 and f(x) < 0
August 1st, 2022
notation
calculus
functions
continuity
Proving continuity of composition of continuous functions
October 18th, 2020
function-and-relation-composition
real-analysis
continuity
Apply the mean value theorem to find the largest possible value of $f(7)$
January 13th, 2020
continuity
calculus
functions
derivatives
continuous function from $\mathbb{Q}$ to $\mathbb{R}$
May 11th, 2020
continuity
When can a function be said to be bounded
August 1st, 2022
real-numbers
real-analysis
continuity
bounded-variation
Show that the function $f$ is attain its minimum or maximum value and bounded on $\mathbb R$
January 14th, 2020
proof-explanation
continuity
How to draw the graph of f(x)= [sin x] + [sin 2x]
August 1st, 2022
continuity
graphing-functions
trigonometry
One-to-one functions on a closed interval
August 1st, 2022
continuity
calculus
How to find the removeable or infinite discontinuity of any rational function without the factoring of the polynomial?
May 3rd, 2020
limits
continuity
calculus
Epsilon delta definition: $\lim _{x\to-2} (2x^2+5x+3)=1$
August 1st, 2022
definition
continuity
limits
Derivative inequality for a twice continuously differentiable function.
August 1st, 2022
real-analysis
continuity
derivatives
calculus
Show that $\cos(1 / x)$ cannot be continuously extended to $0$
April 8th, 2020
continuity
sequences-and-series
real-analysis
prove that $f$ is continuous on $A$ if and only if $f^{-1}(V)$is open in $\Bbb R^n$ for every open subset $V$ of $\Bbb R^m$
August 1st, 2022
analysis
calculus
real-analysis
general-topology
continuity
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