Question

Solve ${lim}_{m\to \infty }{\left(\cos \frac{x}{m}\right)}^m$

• A. $0$
• B. $e$
• C. $1/e$
• D. $1$

Answer 1

The correct option is A $0$

${lim}_{m\to \infty }{\left(\cos \frac{x}{m}\right)}^m$

$={lim}_{m\to \infty }{(1+\frac{\cos x}{m}-1)}^m$

$={lim}_{m\to \infty }{e}^{{(\cos \frac{x}{m}-1)}^m}$

$={lim}_{m\to \infty }{e}^{-\infty }$

$={lim}_{m\to \infty }\frac{1}{e^{\infty }}=0$