Question

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

• A. 1
• B. 2
• C. 4

Answer 1

$\underset{x\to 0}{lim}\frac{x-(x-\frac{x^3}{\angle 3}+\dots \dots )}{x}sin\left(\frac{1}{x}\right)$
$=\underset{x\to 0}{lim}{x}^{2}sin\left(\frac{1}{x}\right).(\frac{1}{\angle 3}+termsofx)$
$=0$