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:

$\displaystyle 64$

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]:                                                                     $\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \lim_{x \to 0} f(x) = 4$

Step 2: Solve

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

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

Unit: Limits

Book: College Calculus 10e