Difference between the limit of function and continuous function
133265
Definition of continuity at a point
143174
property of continuous function
77239
Limit point versus limit and implications for convergence
106060
If $f$ is continuous and with a limit at infinity then $f$ is uniformly continuous
125754
Proving or disproving a statement about continuity and limits
77623
Limit of ratio ${f(x)\over x}$ equal to limit of difference $f(x+1)-f(x)$.
116663
If f is a continuous map from X to Y with X limit point compact, does it follow that f(X) is limit point compact?
48891
Show that: lim$_{n\rightarrow \infty}\,f(x_n)=f(\text{lim}_{n \rightarrow \infty} \, x_n)$
45395
Difference between continuity and uniform continuity
38692
Please clear up this misunderstanding I have involving limits.
108929
Proving the limit of a function of a sequence is equal to the function of the limit of that sequence
33486
Negation of the Definition of Limit of a Function
59839
In $\epsilon$-$\delta$ continuity over an interval, $|x-c|<\delta$ implies $|f(x)-f(c)|<\epsilon$. Since both $c$ and $x$ vary, what's the difference?
97256
For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
6620
If $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x)) =L<\infty$, does $\lim\limits_{x\rightarrow\infty} f(x) $ exist?
49460
Find the limit of the given function
140445
Sequence of continuous functions whose pointwise limit is discontinuous