1. ## Calculus Limits Problem

Find the limits:

a) lim (2x)/(sqrt((x^2)+1))
x-->infinity

b) lim (2x)/(sqrt((x^2)+1))
x-->-infinity

2. Limits to infinity take the highest power of x of the numerator and denominator.

$\displaystyle \lim_{x\to\infty}\frac{2x}{\sqrt{x^2}}=\lim_{x\to\ infty}\frac{2x}{x}=2$

Remember $\displaystyle \sqrt{x^2}=\pm x$. Now, try b.