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

Given limit f(x) = 4 as x approaches 0. What is limit 1/4[f(x)]^4 as x approaches-example-1
User Msapkal
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2 Answers

4 votes

Answer: C. 64

Explanation:

Edge 100%

3 votes

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)

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

User Bholendra Singh
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