Question

$\underset{x\to \infty }{lim}\frac{2+2x+sin2x}{x}is$

• A. equal to zero
• B. equal to 1
• C. equal to -1
• D. 2

Answer 1

Answer: (D)

2

$\underset{x\to \infty }{lim}\frac{2+2x+\sin 2x}{x}$
$=\underset{x\to \infty }{lim}\left(\frac{2}{x}\right)+\underset{x\to \infty }{lim}2+\underset{x\to \infty }{lim}\left(\frac{\sin 2x}{x}\right)$
$=2+0+\underset{x\to \infty }{lim}\frac{\sin 2x}{x}=2$