Changing to $\frac00$ form

Question

Given a and b are two positive constants and the following equation. Find $$\lim_{x\to0}\frac{bx^3-x^2e\sin x}{\sqrt{a+2x^5}}= \frac{1}{π}$$

Have to use L'Hôpital's rule, but have no idea to change the denominator to be 0.

Answer 1

There is no need for l'Hôpital, unless $a=0$. $$\lim_{x\rightarrow 0}\frac{bx^3-x^2e\sin(x)}{\sqrt{a+2x^5}}=\frac{0}{\sqrt{a}}=0$$