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

-1/20

Explanation:

As x approaches c,

g(x) 1/5

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

f(x) -4

Answer 2

`\displaystyle (-1)/(20)`

General Formulas and Concepts:

Calculus

Limit Property [Division]:
`\displaystyle \lim_(x \to c) (f(x))/(g(x)) = ( \lim_(x \to c) f(x))/( \lim_(x \to c) g(x))`

Explanation:

Step 1: Define

Identify

`\displaystyle \lim_(x \to c) f(x) = -4`

`\displaystyle \lim_(x \to c) g(x) = (1)/(5)`

Step 2: Solve

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

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

Unit: Limits

Book: College Calculus 10e