Integrate the function $\frac{1}{\pi }\cdot \left(\frac{1}{2\cdot \left(\frac{9}{4}\right)}+\frac{1}{10+\frac{9}{4}}+\frac{1}{20}+\frac{1}{30}+\frac{1}{40}\right)$

Find the limit

$\lim_{x\to\infty}\left(\frac{7x+8}{4x+3}\right)$

Find the limit

$\lim_{x\to\infty}\left(\frac{e^x}{x^2}\right)$

Find the limit

$\lim_{x\to\infty}\left(\frac{ln\left(x\right)}{\sqrt{x}}\right)$

Find the limit

$\lim_{x\to\infty}\left(xsin\left(\frac{\pi}{x}\right)\right)$

Find the limit

$\lim_{x\to\infty}\left(x^2e^{-x}\right)$

Find the limit

$\lim_{x\to\infty}\left(\frac{\ln\left(x\right)}{x^2}\right)$

Find the limit

$\lim_{x\to\infty}\left(xsin\left(\frac{1}{x}\right)\right)$