Question

$\underset{x\to 0}{lim}\left(\frac{x-sinx}{x}\right)sin\left(\frac{1}{x}\right)$

• A. Equals-1
• B. Equals 1
• C. Does not exist
• D. Equals 0

Answer 1

The correct option is D Equals 0

${lim}_{x\to 0}\left(\right(\frac{x-sinx}{x}\left)\right)sin\left(\frac{1}{x}\right)={lim}_{x\to 0}(1-(\frac{sinx}{x}\left)\right)sin\left(\frac{1}{x}\right)foranyvalueofx,sin\left(\frac{1}{x}\right)\in [-1,1]=0\times finitevalue=0$

So, the correct option is 'Equals 0'