query: Limit of bounded function
positive_passages.docid: 38831
positive_passages.text: If $\lim_{x\to+\infty}[f(x+1)-f(x)]= \ell,$ then $\lim\limits_{x\to+\infty}\frac{f(x)}x=\ell$.
negative_passages.docid: 89180
negative_passages.text: limit of reciprocal of function
negative_passages.docid: 109732
negative_passages.text: Nowhere continuous function limit
negative_passages.docid: 119145
negative_passages.text: $\lim\limits_{n\rightarrow\infty} \sqrt{n}(\sqrt{n+1}-\sqrt{n})$
negative_passages.docid: 82745
negative_passages.text: Showing Entire Function is Bounded
negative_passages.docid: 21070
negative_passages.text: Lim inf with norm and weak convergence
negative_passages.docid: 135999
negative_passages.text: One sided limit of an increasing function defined on an open interval
negative_passages.docid: 22641
negative_passages.text: Nonlinear function continuous but not bounded
negative_passages.docid: 2118
negative_passages.text: Are continuous functions with compact support bounded?
negative_passages.docid: 113151
negative_passages.text: Does $\sum\limits_{i=1}^{\infty}|a_i||x_i| < \infty$ whenever $\sum\limits_{i=1}^{\infty} |x_i| < \infty $ imply $(a_i)$ is bounded?
negative_passages.docid: 83863
negative_passages.text: What is the limit of
negative_passages.docid: 123918
negative_passages.text: Real Analysis, Existence of a Limit Boundedly:$|\int_0^b\frac{sin(ax)}{x}dx | \le c$
negative_passages.docid: 45988
negative_passages.text: limit of Holder norms: $\sup\limits_{x\in [a,b]} f(x) = \lim\limits_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$
negative_passages.docid: 78444
negative_passages.text: Limit of definite integral of $f(x)\cos(mx)$
negative_passages.docid: 4289
negative_passages.text: $\lim_{x\to0}\dfrac{1}{x}-\lim_{x\to0}\dfrac{1}{x}$
negative_passages.docid: 122485
negative_passages.text: Limit of $f(x+\sqrt x)-f(x)$ as $x \to\infty$ if $|f'(x)|\le 1/x$ for $x>1$
negative_passages.docid: 149862
negative_passages.text: Limit of function with natural logarithm