Mathematics - Limits Question with Solution | TestHub

${\lim }_{x\to 0}\frac{f(x)}{x^3}$
Using L Hopital Rule. ${\lim }_{x\to 0}\frac{f^{\prime }(x)}{3x^2}={\lim }_{x\to 0}\frac{x+\sin \left(1-e^x\right)}{3x^2}$ (Again L Hopital) Using L.H. Rule $\begin{array}{rl}& =\underset{x\to 0}{\lim }\frac{-\left[\sin \left(1-e^x\right)\left(-e^x\right)\cdot e^x+\cos \left(1-e^x\right)\cdot e^x\right]}{6}\\ & =-\frac{1}{6}\end{array}$