New posts in Limits

Convergent Improper integral whose integrand tends to a non zero finite limit as x tends to infinity.

If $\lim (f(x) + 1/f(x)) = 2 $ prove that $\lim_{x \to 0} f(x) =1 $

If $\sum_{n=1}^{\infty} a_{n}$ converges, then$\sum_{n=1}^{\infty} \sin(a_{n})$ also converges

Find $\lim\limits_{x \to \infty}{\mathrm{e}^{-x}\int_{0}^{x}{f\left(y\right)\mathrm{e}^{y}\,\mathrm{d}y}}$

Why is $\int_{0}^{1}{(1+x^2)^n dx} \sim \frac{2^n}{n} $?

Evaluating $\lim_{x \to \frac{\pi}{6}}{(1-2\sin(x))}^{\tan(\frac{\pi}{6}-x)}$

Evaluating $\lim_{n \to \infty} \int_{0}^{\pi} \frac{\sin x}{1+\cos ^2(nx)} dx$

Prove $\lim_{n \to \infty}\int_0^1 \dots \int_0^1 f(\sqrt[n]{x_1\dots x_n})dx_1\dots dx_n = f(\frac{1}{e}).$ $f$ is continuous on $[0;1].$

Calculating $\lim_n e^{-inz}$

Regarding evaluation of the limit of the sequence $\Bigl(\frac{1}{n}\Bigr)^n+\Bigl(\frac{2}{n}\Bigr)^n+ \cdots \Bigl(\frac{n}{n}\Bigr)^n$