Prove that if f is continous on R and the limit as x approaches infinity and negative infinity is infinity, then f obtains its minimum value in R?
91398
Continuous function on R which tends to infinity on open interval must have a minimum
149853
What infinity is greater than the continuum? Show with an example
5371
If a function has a finite limit at infinity, does that imply its derivative goes to zero?
36248
A classical problem about limit of continuous function at infinity and its connection with Baire Category Theorem
83707
Suppose that $f$ is differentiable on $\mathbb{R}$ and $\lim_{x\to \infty}f'(x)=M$. Show that $\lim_{x\to \infty}f(x+1)-f(x)$ exists and find it.
32063
if $f'(x)\rightarrow L$ as $ x \rightarrow \infty$, $-\infty \leq L \leq \infty $ then $ f(x)/x \rightarrow L $ as $x \rightarrow \infty$
31931
limit as $x$ approaches infinity of $\frac{1}{x}$
132824
Does $f$ monotone and $f\in L_{1}([a,\infty))$ imply $\lim_{t\to\infty} t f(t)=0$?
119602
$f:\mathbb{R} \to \mathbb{R}$ be differentiable and $\lim\limits_{x\to\infty}f'(x)=1$, is $f(x)$ unbounded?
42817
proving $\lim\limits_{n\to\infty} \int_{0}^{1} f(x^n)dx = f(0)$ when f is continous on [0,1]
91523
Prove this limit as $x\to\infty$
110395
Integrable function $f$ on $\mathbb R$ does not imply that limit $f(x)$ is zero
37055
Show that $\lim _{r \to 0} \|T_rf−f\|_{L_p} =0.$
154034
Suppose that $f(x)$ is continuous on $(0, \infty)$ such that for all $x > 0$,$f(x^2) = f(x)$. Prove that $f$ is a constant function.
66441
Prove that $|x|<1$ implies that $\lim_{n \to \infty} x^n=0$
125821
Evaluating limits at positive and negative infinity
53627
Proving continuity of $f$