Suppose that $f: \mathbb{R^+}\to \mathbb{R}$ satisfies $\lim_{x\to \infty} (f+f')(x)=0$. Show that $\lim_{x\to \infty} f(x)=0$.
19986
How can this be proved $\lim_{x\to\infty}(f(x)+f'(x))=l$
854
$\lim_{n\to\infty}a_nb_n=? $ given that $\lim_{n\to\infty}a_n=0$ and $\lim_{n\to\infty}b_n=\infty$
133386
If $f$ is entire and $\lim_\limits{z\to\infty} \frac{f(z)}{z} = 0$ show that $f$ is constant
53236
Formal proof of $\lim_{x\to a}f(x) = \lim_{h\to 0} f(a+h)$
81
$\lim_{n\to \infty}f(nx)=0$ implies $\lim_{x\to \infty}f(x)=0$
149586
If $\lim_{x\to\infty} f'(x) = L$, prove that $\lim_{x\to\infty} f(x+c)-f(x) = cL$ and $\lim_{x\to\infty} f(x)/x=L$
135700
Show that $\lim_{n \to \infty} (1/n)\sum_{i=1}^n f(x_i)$ exists
129579
If $f''(x_0)$ exists then $\lim_{x \to x_0} \frac{f(x_0+h)-2f(x_0)+f(x_0-h)}{h^2} = f''(x_0)$
110395
Integrable function $f$ on $\mathbb R$ does not imply that limit $f(x)$ is zero
114747
If $\lim_{x \to \infty}f'(x)=+\infty$ then $\lim_{x \to \infty}(f(x)-f(x-1))=+\infty$ and $\lim_{x \to \infty}f(x)=+\infty$.
41173
If $f\in S_\infty$ and $\int_{\mathbb{R}}x^pf(x)d\mu=0$ for all $p\in\mathbb{N}$ then $f\equiv 0$?
132824
Does $f$ monotone and $f\in L_{1}([a,\infty))$ imply $\lim_{t\to\infty} t f(t)=0$?
67292
Prove that $\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$
44060
If $\lim_{x \to +\infty} f'(x) = L$, then $\lim_{x \to \infty} \frac {f(x)}{x} = L$
33337
$\int_{0}^{\infty} f(x) \,dx$ exists. Then $\lim_{x\rightarrow \infty} f(x) $ must exist and is $0$. A rigorous proof?
49929
If $ \lim_{n \to \infty} (2 x_{n + 1} - x_{n}) = x $, then is it true that $ \lim_{n \to \infty} x_{n} = x $?
35325
Prove that $\lim_{n\to\infty}\frac1{n}\int_0^{n}xf(x)dx=0$.