If a derivative of a continuous function has a limit, must it agree with that limit?
1371
Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
11385
Using the Limit definition to find the derivative of $e^x$
118048
Can a function with just one point in its domain be continuous?
106060
If $f$ is continuous and with a limit at infinity then $f$ is uniformly continuous
95921
Question about $\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}$
5371
If a function has a finite limit at infinity, does that imply its derivative goes to zero?
123981
Is it possible to write any bounded continuous function as a uniform limit of smooth functions
87819
What is the difference between continuous derivative and derivative?
58361
Is there a continuous function such that $\int_0^{\infty} f(x)dx$ converges, yet $\lim_{x\rightarrow \infty}f(x) \ne 0$?
77239
Limit point versus limit and implications for convergence
44647
Does pointwise convergence of continuous functions on a compact set to a continuous limit imply uniform convergence on that set?
60321
Use the definition of derivative to prove $\lim_{x\to 0}\ln(x+1)/x =1$
47381
If $\lim_{x\to\infty} [f(x+1)-f(x)] =l$ then $\lim_{ x\to\infty}f(x)/x =l$ ($f$ is continuous)
99906
If $f'(c)$ exists then $\lim_{x\to c} f(x)=f(c)$
32571
Is the maximum function of a continuous function continuous?
9614
How does the existence of a limit imply that a function is uniformly continuous
25482
If a function is continuous and differentiable everywhere is the derivative continuous?