Question

${lim}_{x\to 0}\frac{x-sinx}{1-cosx}$ is

• A. 0
• B. 1
• C. 3
• D. not defined

Answer 1

The correct option is A 0

${lim}_{x\to 0}\frac{x-sinx}{1-cosx}={lim}_{x\to 0}\frac{1-cosx}{sinx}\left(\frac{0}{0}\right)$

$={lim}_{x\to 0}\frac{sinx}{cosx}=\frac{0}{1}$

$={lim}_{x\to 0}\frac{x-sinx}{1-cosx}=0$