Question

The value of ${lim}_{x\to \infty }\frac{x+\cos x}{x+\sin x}$ is

• A. $-1$
• B. $0$
• C. $1$
• D. None of these

Answer 1

The correct option is C $1$

${lim}_{x\to \infty }\frac{x+\cos x}{x+\sin x}$

Divide numerator and denominator by $x$

$={lim}_{x\to \infty }\frac{1+\left(\frac{\cos x}{x}\right)}{1+\left(\frac{\sin x}{x}\right)}$

$=\frac{1+{lim}_{x\to \infty }\left(\frac{\cos x}{x}\right)}{1+{lim}_{x\to \infty }\left(\frac{\sin x}{x}\right)}$

$=\frac{1+0}{1+0}$

$=1$