Question

Evaluate the limit:

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

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

Answer 1

The correct option is D $0$

${lim}_{x\to 0}\left(\frac{x-\sin x}{x}\right)\sin \left(\frac{1}{x}\right){lim}_{x\to 0}\left(\frac{x-\sin x}{x}\right)\times {lim}_{x\to 0}\sin \left(\frac{1}{x}\right)(1-\cos x)\times (Valuebetween-1and1)0\times Valuebetween(-1\&1)0$