Question

Given limit f(x) = 4 as x approaches 0. What is limit 1/4[f(x)]^4 as x approaches 0?

Answer 1

Answer: C. 64

Explanation:

Edge 100%

Answer 2

`\displaystyle 64`

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:
`\displaystyle \lim_(x \to c) x = c`

Limit Rule [Variable Direct Substitution Exponential]:
`\displaystyle \lim_(x \to c) x^n = c^n`

Limit Property [Multiplied Constant]:
`\displaystyle \lim_(x \to c) bf(x) = b \lim_(x \to c) f(x)`

Explanation:

Step 1: Define

Identify

`\displaystyle \lim_(x \to 0) f(x) = 4`

Step 2: Solve

1. Rewrite [Limit Property - Multiplied Constant]:
   `\displaystyle \lim_(x \to 0) (1)/(4)[f(x)]^4 = (1)/(4) \lim_(x \to 0) [f(x)]^4`
2. Evaluate limit [Limit Rule - Variable Direct Substitution Exponential]:
   `\displaystyle \lim_(x \to 0) (1)/(4)[f(x)]^4 = (1)/(4)(4^4)`
3. Simplify:
   `\displaystyle \lim_(x \to 0) (1)/(4)[f(x)]^4 = 64`

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

Unit: Limits

Book: College Calculus 10e