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5 (x+4)³ For the function f(x) = exist, enter Ø as your answer. X -4.1 -4.01 -4.001 -4.0001 -4.00001 evaluate the left and right limits using the table shown below. If any of the limits do not I 5 5 X (x+4)³ (x+4)³ 5000 -3.9 -5000 5000000 -3.99 -5000000 5000000000 -3.999 -5000000000 5000000000000 -3.9999 -5000000000000 5000000000000000 -3.99999 -5000000000000000

5 (x+4)³ For the function f(x) = exist, enter Ø as your answer. X -4.1 -4.01 -4.001 -4.0001 -4.00001 evaluate the left and right limits using the table shown below. If any of the limits do not I 5 5 X (x+4)³ (x+4)³ 5000 -3.9 -5000 5000000 -3.99 -5000000 5000000000 -3.999 -5000000000 5000000000000 -3.9999 -5000000000000 5000000000000000 -3.99999 -5000000000000000

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Question** For the function \( f(x) = \frac{-5}{(x + 4)^3} \), evaluate the left and right limits using the table shown below. If any of the limits do not exist, enter ∅ as your answer. **Table:** \[ \begin{array}{|c|c|c|c|} \hline x & \frac{-5}{(x + 4)^3} & x & \frac{-5}{(x + 4)^3} \\ \hline -4.1 & 5000 & -3.9 & -5000 \\ \hline -4.01 & 5000000 & -3.99 & -5000000 \\ \hline -4.001 & 5000000000 & -3.999 & -5000000000 \\ \hline -4.0001 & 5000000000000 & -3.9999 & -5000000000000 \\ \hline -4.00001 & 500000000000000 & -3.99999 & -500000000000000 \\ \hline \end{array} \] **Explanation of the Table:** The table has two main sections, each representing values of \( x \) approaching \(-4\) from either the left (values less than \(-4\)) or the right (values greater than \(-4\)). The corresponding values of the function \( f(x) = \frac{-5}{(x + 4)^3} \) are calculated for each \( x \). - As \( x \) approaches \(-4\) from the left (values less than \(-4\)), the function values become increasingly positive. For example: - When \( x = -4.1 \), \( \frac{-5}{(x + 4)^3} = 5000 \). - When \( x = -4.01 \), \( \frac{-5}{(x + 4)^3} = 5000000 \). - When \( x = -4.001 \), \( \frac{-5}{(x + 4)^3} = 5000000000 \). - As \( x \) approaches \(-4\) from the right (values greater than \(-
Transcribed Image Text:**Question** For the function \( f(x) = \frac{-5}{(x + 4)^3} \), evaluate the left and right limits using the table shown below. If any of the limits do not exist, enter ∅ as your answer. **Table:** \[ \begin{array}{|c|c|c|c|} \hline x & \frac{-5}{(x + 4)^3} & x & \frac{-5}{(x + 4)^3} \\ \hline -4.1 & 5000 & -3.9 & -5000 \\ \hline -4.01 & 5000000 & -3.99 & -5000000 \\ \hline -4.001 & 5000000000 & -3.999 & -5000000000 \\ \hline -4.0001 & 5000000000000 & -3.9999 & -5000000000000 \\ \hline -4.00001 & 500000000000000 & -3.99999 & -500000000000000 \\ \hline \end{array} \] **Explanation of the Table:** The table has two main sections, each representing values of \( x \) approaching \(-4\) from either the left (values less than \(-4\)) or the right (values greater than \(-4\)). The corresponding values of the function \( f(x) = \frac{-5}{(x + 4)^3} \) are calculated for each \( x \). - As \( x \) approaches \(-4\) from the left (values less than \(-4\)), the function values become increasingly positive. For example: - When \( x = -4.1 \), \( \frac{-5}{(x + 4)^3} = 5000 \). - When \( x = -4.01 \), \( \frac{-5}{(x + 4)^3} = 5000000 \). - When \( x = -4.001 \), \( \frac{-5}{(x + 4)^3} = 5000000000 \). - As \( x \) approaches \(-4\) from the right (values greater than \(-
### Limit Evaluation Practice Problems Provide your answer below: **Question a:** \[ \lim_{{x \to -4^-}} f(x) = \Box \] **Question b:** \[ \lim_{{x \to -4^+}} f(x) = \Box \] **Question c:** \[ \lim_{{x \to -4}} f(x) = \Box \] ### Instructions: Evaluate the given limits for the function \( f(x) \) as \( x \) approaches \(-4\) from the left, right, and both sides respectively. Fill in the boxes with your answers.
Transcribed Image Text:### Limit Evaluation Practice Problems Provide your answer below: **Question a:** \[ \lim_{{x \to -4^-}} f(x) = \Box \] **Question b:** \[ \lim_{{x \to -4^+}} f(x) = \Box \] **Question c:** \[ \lim_{{x \to -4}} f(x) = \Box \] ### Instructions: Evaluate the given limits for the function \( f(x) \) as \( x \) approaches \(-4\) from the left, right, and both sides respectively. Fill in the boxes with your answers.
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