Question

If $\underset{x\to 0}{lim}\frac{x^a{\sin }^{b}x}{\left({\sin }^{c}x\right)}$, where $a,b,c\in R-\left\{0\right\}$ exists & has non zero value then $a+b=c$.
If true enter 1 else enter 0

Answer 1

$\underset{x\to 0}{lim}{x}^a\frac{{\sin }^{b}x}{{\sin }^{c}x}=\underset{x\to 0}{lim}\frac{{\sin }^{b-c}x}{x^{-a}}$
Given the limit exists.
$\therefore b-c=-a\Rightarrow a+b=c$