If the function f(x)=( ( x)- ( x))/( x- x) is continuous at x=0, then f(0) is equal to ___…

Question

If the function $f(x)=\frac{	an (	an x)-\sin (\sin x)}{	an x-\sin x}$ is continuous at $x=0$, then $f(0)$ is equal to \_\_\_\_\_\_\_\_\_\_\_\_.

Answer: 2

Accepted Answer

$\underset{x	o 0}{lim}\frac{\frac{	an (	an x)-	an x}{{	an }^{3}x}\frac{{	an }^{3}x}{{x}^{3}}+\frac{	an x-\sin x}{{x}^{3}}+\frac{\sin x-\sin (\sin x)}{{\sin }^{3}x}\frac{{\sin }^{3}x}{{x}^{3}}}{\frac{	an x-\sin x}{{x}^{3}}}$

$=\frac{\frac{1}{3}+\frac{1}{2}+\frac{1}{6}}{\frac{1}{2}}=2$

Solutions · 1