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...
Related questions
Question
![### Limit Calculation Problem
Consider the piecewise function \( f(x) \) defined as follows:
\[
f(x) =
\begin{cases}
-6x - 15 & \text{if } x < -3 \\
13 & \text{if } x = -3 \\
2x^2 - 15 & \text{if } x > -3
\end{cases}
\]
#### Task
Calculate the following limit. Enter "DNE" (Does Not Exist) if the limit does not exist.
\[
\lim_{x \to -3} f(x) = \_\_\_\_\_\_
\]
[Submit Question]
---
To solve this exercise, evaluate the limit of \( f(x) \) as \( x \) approaches \(-3\) from both the left and the right. Consider continuity and the behavior of the piecewise functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F868b8534-4d89-4d63-908b-b662dc9aeef4%2F143d6bc9-8eb9-4532-bc6e-96c22dbab4fa%2Feklumn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Limit Calculation Problem
Consider the piecewise function \( f(x) \) defined as follows:
\[
f(x) =
\begin{cases}
-6x - 15 & \text{if } x < -3 \\
13 & \text{if } x = -3 \\
2x^2 - 15 & \text{if } x > -3
\end{cases}
\]
#### Task
Calculate the following limit. Enter "DNE" (Does Not Exist) if the limit does not exist.
\[
\lim_{x \to -3} f(x) = \_\_\_\_\_\_
\]
[Submit Question]
---
To solve this exercise, evaluate the limit of \( f(x) \) as \( x \) approaches \(-3\) from both the left and the right. Consider continuity and the behavior of the piecewise functions.
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