New posts in Limits

Asymptotic behaviour of $\int_0^{\infty } x^{-x} \exp (n x) dx$

Asymptotic expansion of $\sum _{k=1}^n \left(\frac{k}{n}\right)^k$

Find $\lim\limits_{n \to \infty} n \int_2^e (\ln x)^n \, dx$.

How do we know the Riemann Sum gives us the area under the curve?

Asymptotic expansion of $f(x)=\sum _{n=1}^{\infty } \frac{\sin \left(\sqrt{n}x\right)}{n}$ at the origin

Find $\lim_{x \to \infty} x^3 \left ( \sin\frac{1}{x + 2} - 2 \sin\frac{1}{x + 1} + \sin\frac{1}{x} \right )$

Find limit $\lim_{n\to\infty}\sum_{k=n}^{5n}{k-1\choose n-1}\left(\frac{1}{5}\right)^{n}\left(\frac{4}{5}\right)^{k-n}$

Limit $\lim_{n\to\infty}\sum_{k=0}^n\frac{n^{2k}}{(k!)^2}\big/\sum_{k=0}^\infty\frac{n^{2k}}{(k!)^2}$

Find $\lim_{x\to0} \frac{\log(1+3x)}{f(x)}$ given $\lim_{x\to0} \frac{f(x)}{\sin(x)} = 2$

Every even degree polynomial is eventually symmetric