query: Let be $f$ a continuous function. Determine the limit $\lim\limits_{h \to 0} \frac{1}{h} \int_{a-h}^{a+h} f(x)\,dx$
positive_passages.docid: 157308
positive_passages.text: Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be continuous.Let $t\in\mathbb{R}$. Evaluate:$\lim_{h\rightarrow0}\frac{1}{h}\int_{t-h}^{t+h}f(s)ds$
negative_passages.docid: 51231
negative_passages.text: Find the limit of $\frac{n^{x}}{(1 + x)^{n}}$
negative_passages.docid: 127125
negative_passages.text: Can the limit $\lim_{h \to 0}\frac{f(x + h) - 2f(x) + f(x - h)}{h^2}$ exist if $f'(x)$ does not exist at $x$?
negative_passages.docid: 111929
negative_passages.text: Find the limit: $\lim_\limits{x\to 0}{\frac{\left(1+x\right)^{1/x}-e}{x}}$
negative_passages.docid: 53236
negative_passages.text: Formal proof of $\lim_{x\to a}f(x) = \lim_{h\to 0} f(a+h)$
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: 134787
negative_passages.text: How to prove $\lim \limits_{n\to\infty}(n+1)\int_{0}^{1}x^nf(x)dx=f(1)$
negative_passages.docid: 4289
negative_passages.text: $\lim_{x\to0}\dfrac{1}{x}-\lim_{x\to0}\dfrac{1}{x}$
negative_passages.docid: 145233
negative_passages.text: How to show $\lim_{n \rightarrow \infty} \int_0^1 n x^n f(x) \; dx = f(1)$ for continuous $f$?
negative_passages.docid: 11382
negative_passages.text: Limit $\lim\limits_{x\to0}\frac1{\ln(x+1)}-\frac1x$
negative_passages.docid: 147184
negative_passages.text: $f:[-1,1]\to \mathbb{R}$ is a continuous function such that $f(2x^2-1)=(x^3+x)f(x).$ Find $\lim_{x\to 0}\frac {f(\cos x)}{\sin x}$
negative_passages.docid: 5167
negative_passages.text: Finding the limit that involves Fourier coefficients,
negative_passages.docid: 109907
negative_passages.text: How to prove that $\lim\limits_{h \to 0} \frac{a^h - 1}{h} = \ln a$
negative_passages.docid: 95991
negative_passages.text: How to solve $\lim_{x \rightarrow 0} {\frac{(1+x)^a-1}{x}}$?
negative_passages.docid: 113289
negative_passages.text: finding the limit $\lim\limits_{x \to \infty }(\frac{1}{e}(1+\frac{1}{x})^x)^x$
negative_passages.docid: 9746
negative_passages.text: Determine the following limit as x approaches 0: $\frac{\ln(1+x)}x$
negative_passages.docid: 86634
negative_passages.text: How to find $ \lim_{(x,y)\to(0,0)} \frac{\sin^2 (x-y)}{|x|+|y|} $?