solve {eq}lim _{x \to 0} \frac{(1+sinx)^{1/3} - (1 - 2 tanx)^{1/4}} { (sin x+tan^2x)} {/eq}

Question:

L'Hospital Rule and its Idea:

If we want to find the limit {eq}\mathop {\lim }\limits_{x \to a} \frac{{f\left( x \right)}}{{g\left( x \right)}} {/eq}

Which is of the form either {eq}\left( {\frac{0}{0}} \right) {/eq} or {eq}\left( {\frac{\infty }{\infty }} \right) {/eq}, then by using L'Hospital rule we can say that:

{eq}\mathop {\lim }\limits_{x \to a} \frac{{f\left( x \right)}}{{g\left( x \right)}} = \mathop {\lim }\limits_{x \to a} \frac{{f'\left( x \right)}}{{g'\left( x \right)}} {/eq}

Answer and Explanation: 1