Question

Given limit of f(x) = -4 as x approaches c and limit of g(x) =1/5 as x approaches c. What is limit of g(x)/f(x) as x approaches c?

Answer 1

Answer:

$\displaystyle \frac{-1}{20}$

General Formulas and Concepts:

Calculus

Limit Property [Division]:                                                                                              $\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \frac{ \lim_{x \to c} f(x)}{ \lim_{x \to c} g(x)}$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \lim_{x \to c} f(x) = -4$

$\displaystyle \lim_{x \to c} g(x) = \frac{1}{5}$

Step 2: Solve

1. Substitute in limits [Limit Property - Division]:                                                $\displaystyle \lim_{x \to c} \frac{g(x)}{f(x)} = \frac{ \frac{1}{5} }{ -4 }$
2. Simplify:                                                                                                             $\displaystyle \lim_{x \to c} \frac{g(x)}{f(x)} = \frac{-1}{20}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

Answer 2

Answer:

-1/20

Step-by-step explanation:

As x approaches c,

g(x)         1/5

------ = ------------ = -1/20            (matches last of the four given possible answers)

f(x)          -4