Question

$\underset{x\to 0}{lim}\frac{\left[\frac{x}{sinx}\right]-\left[\frac{sinx}{x}\right]}{\left[\frac{tanx}{x}\right]}$ is equal to $([.]$represents the greatest integer function) -

• A. $1$
• B. $-1$
• C. $0$
• D. does not exists

Answer 1

The correct option is A $1$

$\Rightarrow \underset{x\to 0}{lim}\left[\frac{x}{sinx}\right]=1$

$\Rightarrow \underset{x\to 0}{lim}\left[\frac{sinx}{x}\right]=0$

$\Rightarrow \underset{x\to 0}{lim}\left[\frac{tanx}{x}\right]=1$

$\Rightarrow \underset{x\to 0}{lim}\frac{\left[\frac{x}{sinx}\right]-\left[\frac{sinx}{x}\right]}{\left[\frac{tanx}{x}\right]}=1$