સરવાળાની મર્યાદા તરીકે $\int_2^3 x^2 dx$ ની કિંમત શોધો.

$\lim _{n \rightarrow \infty}\left[\frac{1^k+2^k+3^k+\ldots+n^k}{n^{k+1}}\right]=$

$\lim _{n \rightarrow \infty}\left[\frac{1}{n}+\frac{n^2}{(n+1)^3}+\frac{n^2}{(n+2)^3}+\frac{n^2}{(n+3)^3}+\ldots+\frac{n^2}{(n+4n)^3}\right]=$

$\lim _{n}$ ${\rightarrow \infty} \left( \frac{\sqrt{n}}{\sqrt{n^{3}}}+\frac{\sqrt{n}}{\sqrt{(n+4)^{3}}}+\frac{\sqrt{n}}{\sqrt{(n+8)^{3}}}+\cdots +\frac{\sqrt{n}}{\sqrt{[n+4(n-1)]^{3}}} \right)$ ની કિંમત શોધો.

$\lim _{n}$ ${\rightarrow \infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{2^2}{n^2}\right) \ldots \left(1+\frac{n^2}{n^2}\right)\right]^{1 / n}=$

$\lim _{n \rightarrow \infty} \left[ \frac{n}{n^{2}+1^{2}} + \frac{n}{n^{2}+2^{2}} + \ldots + \frac{n}{n^{2}+n^{2}} \right]$ ની કિંમત શોધો.