Question

The value of $\underset{x\to \pi }{lim}\left(x\cos x\right)$ is

• A. $\pi$
• B. $0$
• C. $-\pi$
• D. limit does not exist

Answer 1

The correct option is C $-\pi$

We know that
$\underset{x\to a}{lim}(f\left(x\right)\cdot g\left(x\right))=\underset{x\to a}{lim}f\left(x\right)\cdot \underset{x\to a}{lim}g\left(x\right)$

$\therefore \underset{x\to \pi }{lim}\left(x\cos x\right)=\left(\underset{x\to \pi }{lim}x\right)\left(\underset{x\to \pi }{lim}\cos x\right)=\pi \left(\cos \pi \right)=-\pi$