query: $\lim_n{f(\frac{x}{n})}=0$, for all $x\in (0,1)$ implies $lim_{x\to0}f(x)=0$ (edit, $f$ is not continuous)
positive_passages.docid: 29180
positive_passages.text: If $f(x/n)\to0$ when $n\to\infty$, for every $x$ and $f$ is continuous, then $f(x)\to0$ when $x\to0$, or not?
negative_passages.docid: 80277
negative_passages.text: How to show that $\lim \frac{1}{n} \sum_{i=1}^n \frac{1}{i}=0 $?
negative_passages.docid: 120777
negative_passages.text: How to formally prove that if $\lim \limits_{n \to \infty}a_n=\infty$, then $\lim \limits_{n \to \infty}\frac{1}{a_n}=0$.
negative_passages.docid: 73812
negative_passages.text: Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?
negative_passages.docid: 75735
negative_passages.text: Let $f$ be a continuous function on an interval around $0$ and let $a_i=f(\frac{1}{i})$ (for large enough $i$)
negative_passages.docid: 34187
negative_passages.text: The limit of the derivative of an increasing and bounded function is always $0$?
negative_passages.docid: 119200
negative_passages.text: When does $\lim_{n\to\infty}f(x+\frac{1}{n})=f(x)$ a.e. fail
negative_passages.docid: 9614
negative_passages.text: How does the existence of a limit imply that a function is uniformly continuous
negative_passages.docid: 67364
negative_passages.text: If $\lim_{x\to\infty}(f(x)+f'(x))=L$ show that $\lim_{x\to\infty} f(x) = L$ and $\lim_{x\to\infty} f'(x) = 0$
negative_passages.docid: 97747
negative_passages.text: Limit of $\lim\limits_{n\to\infty} (1 + \frac{x_n}{n})^n$
negative_passages.docid: 44336
negative_passages.text: Is $\lim\limits_{x\to x_0}f'(x)=f'(x_0)$?
negative_passages.docid: 15284
negative_passages.text: $f$ defined on $[1,\infty )$ is uniformly continuous. Then $\exists M>0$ s.t. $\frac{|f(x)|}{x}\le M$ for $x\ge 1$.
negative_passages.docid: 47381
negative_passages.text: If $\lim_{x\to\infty} [f(x+1)-f(x)] =l$ then $\lim_{ x\to\infty}f(x)/x =l$ ($f$ is continuous)
negative_passages.docid: 150235
negative_passages.text: $\epsilon$-$\delta$ proof that $f(x) = x \sin(1/x)$, $x \ne 0$, is continuous
negative_passages.docid: 94564
negative_passages.text: If $f$ is bounded and $\lim_{x \to c} g(x) = 0$, then $\lim_{x \to c}g(x)f(x) = 0$
negative_passages.docid: 18153
negative_passages.text: To prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not uniformly converge to $f(x) = 0$ on $[0,1]$
negative_passages.docid: 67292
negative_passages.text: Prove that $\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$