Let f(x)=y 0lim(1- (xy)) (xy)y^3.

Question

Let $f(x)=\underset{y	o 0}{lim}\frac{(1-\cos (xy))	an (xy)}{{y}^{3}}$. Then the number of solutions of the equation $f(x)=\sin x$, $x\in R$ is :

Accepted Answer

$\begin{gathered} f(x)=\underset{y	o 0}{lim}\frac{1-\cos (xy)}{(xy{)}^{2}}\cdot \frac{	an xy}{xy}\frac{(xy{)}^{3}}{{y}^{3}} \ f(x)=\frac{{x}^{3}}{2} \ f(x)=\sin x \ \frac{{x}^{3}}{2}=\sin x \end{gathered}$

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