Question

Find the following limit:
$\underset{x\to \infty }{lim}\frac{{\int }_0^{x}tdt}{x\tan (x+\pi )}$

Answer 1

$\underset{x\to \infty }{lim}\frac{\frac{x^2}{2}}{x\tan (x+\pi )}=\underset{x\to \infty }{lim}\frac{1}{2}\times \underset{x\to \infty }{lim}\frac{x}{\tan \left(x\right)}=\frac{1}{2}$