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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![**Problem Statement:**
Find \(\lim_{{x \to 2}} f(x)\) for
\[
f(x) =
\begin{cases}
2x + 1, & x \leq 2 \\
x^2, & x > 2
\end{cases}
\]
**Answer Choices:**
- O Does not exist
- O 5 or 4
- O 4
- O 5
**Explanation of the Function:**
The function \( f(x) \) is a piecewise function defined for \( x \leq 2 \) and \( x > 2 \). For values of \( x \) less than or equal to 2, the function \( f(x) = 2x + 1 \). For values of \( x \) greater than 2, the function \( f(x) = x^2 \).
The problem asks for the limit of \( f(x) \) as \( x \) approaches 2, taking into account the behavior of both parts of the piecewise function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4bf8d9f8-9f3c-4f11-9f6a-4feeeac00eb3%2F8f48b902-a947-4dca-9add-b8527980563c%2F5nuh4cj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find \(\lim_{{x \to 2}} f(x)\) for
\[
f(x) =
\begin{cases}
2x + 1, & x \leq 2 \\
x^2, & x > 2
\end{cases}
\]
**Answer Choices:**
- O Does not exist
- O 5 or 4
- O 4
- O 5
**Explanation of the Function:**
The function \( f(x) \) is a piecewise function defined for \( x \leq 2 \) and \( x > 2 \). For values of \( x \) less than or equal to 2, the function \( f(x) = 2x + 1 \). For values of \( x \) greater than 2, the function \( f(x) = x^2 \).
The problem asks for the limit of \( f(x) \) as \( x \) approaches 2, taking into account the behavior of both parts of the piecewise function.
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