query: $f \in L^1 \implies \lim_{ |x| \to \infty } f(x) = 0$
positive_passages.docid: 110395
positive_passages.text: Integrable function $f$ on $\mathbb R$ does not imply that limit $f(x)$ is zero
negative_passages.docid: 104269
negative_passages.text: Why does $\lim\limits_{t\to-\infty}te^t=0$?
negative_passages.docid: 19072
negative_passages.text: $\int_{\mathbb R} |f(x)| dx < \infty \implies \int^{\infty}_{n} |f(x)| dx \to 0$ as $n \to \infty$?
negative_passages.docid: 67292
negative_passages.text: Prove that $\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$
negative_passages.docid: 44129
negative_passages.text: If $f:\mathbb{R}\rightarrow \mathbb{R}$ is differentiable and $\lim_{x\to \infty } f^\prime(x)=0$ show that $\lim _{x\to \infty } (f(x+1)-f(x))=0$.
negative_passages.docid: 70790
negative_passages.text: Evaluation of $\lim_{q \to 0} (\int_0^1 |f|^q)^{1/q} $ for $f \in L^1([0,1])$.
negative_passages.docid: 9781
negative_passages.text: How to prove that $\lim_{n \to \infty} n x^{n} = 0 $ when $0<x<1$?
negative_passages.docid: 91680
negative_passages.text: Does $\lim_{n\to \infty} \int^{\infty}_{-\infty} f_n(x) dx\, = \int^{\infty}_{-\infty} f(x)\,dx\,$?
negative_passages.docid: 66441
negative_passages.text: Prove that $|x|<1$ implies that $\lim_{n \to \infty} x^n=0$
negative_passages.docid: 25206
negative_passages.text: How to prove that $\lim\limits_{n\to \infty}a_{n+1}=\lim\limits_{n\to \infty}a_{n}$
negative_passages.docid: 59162
negative_passages.text: Prove $\liminf\limits_{n\to\infty} F(x_n)\le F(x)$
negative_passages.docid: 97256
negative_passages.text: For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
negative_passages.docid: 13732
negative_passages.text: $||f||_p\to ||f||_\infty$ under general assumptions
negative_passages.docid: 25467
negative_passages.text: Prove that $\lim f(x) =0$ and $\lim (f(2x)-f(x))/x =0$ imply $\lim f(x)/x =0$
negative_passages.docid: 149586
negative_passages.text: If $\lim_{x\to\infty} f'(x) = L$, prove that $\lim_{x\to\infty} f(x+c)-f(x) = cL$ and $\lim_{x\to\infty} f(x)/x=L$
negative_passages.docid: 71225
negative_passages.text: $f(0)=0$ and $\lim_{x \to \infty}f(x)=0$. Show there's $x_0$ such that $f'(x_0)=0$
negative_passages.docid: 94564
negative_passages.text: If $f$ is bounded and $\lim_{x \to c} g(x) = 0$, then $\lim_{x \to c}g(x)f(x) = 0$