Aparna Shakti, 3 at Chegg India, Numerade Educator

06:29

Calculus: Early Transcendentals

Given that
$ \displaystyle \lim_{x \to 2}f(x) = 4 $ $ \displaystyle \lim_{x \to 2}g(x) = -2 $ $ \displaystyle \lim_{x \to 2}h(x) = 0 $
find the limits that exist. If the limit does not exist, explain why.

(a) $ \displaystyle \lim_{x \to 2}[f(x) + 5g(x)] $
(b) $ \displaystyle \lim_{x \to 2}[g(x)]^3 $
(c) $ \displaystyle \lim_{x \to 2}\sqrt{f(x)} $
(d) $ \displaystyle \lim_{x \to 2}\frac{3f(x)}{g(x)} $
(e) $ \displaystyle \lim_{x \to 2}\frac{g(x)}{h(x)} $
(f) $ \displaystyle \lim_{x \to 2}\frac{g(x)h(x)}{f(x)} $

Chapter 2: Limits and Derivatives

Section 3: Calculating Limits Using the Limit Laws