Question

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

• A. -1
• B. 1
• C. 0
• D. none of these

Answer 1

Answer: (B)

1

$\underset{x\to \infty }{lim}\sqrt{\frac{x-\sin x}{x+{\cos }^{2}x}}$

$=\underset{x\to \infty }{lim}\sqrt{\frac{1-\frac{\sin x}{x}}{1+\frac{{\cos }^{2}x}{x}}}$

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