Question

$\underset{x\to \infty }{lim}\frac{\cos x+\sin x}{x^2}$ is equal to

• A. $1$
• B. $0$
• C. $\infty$
• D. none of these

Answer 1

Answer: (B)

$0$

${lim}_{a\to \infty }\frac{(\cos x+\sin x)}{x^2}$

$=\frac{(\cos \infty +\sin \infty )}{{\infty }^2}$

We know that

$-\sqrt{2}\le \cos x+\sin x\le \sqrt{2}$ (a is finite and lies between $-\sqrt{2}$ and $\sqrt{2}$)

$=\frac{a}{{\infty }^2}=0$