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
Just want to make sure my answer is correct. How do you find H?
![Find the value of \( k \) that will make the function \( f(x) \) continuous everywhere.
\[
f(x) =
\begin{cases}
2x + k, & x \leq 2 \\
kx^2 - 5, & x > 2
\end{cases}
\]
Options:
- \( \frac{1}{8} \)
- 2
- such a \( k \) does not exist
- -3
- 3
[Explanation: The question presents a piecewise function \( f(x) \) with different expressions for \( x \leq 2 \) and \( x > 2 \). The task is to find a value of \( k \) that ensures the function is continuous across all values of \( x \).]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc388c4d9-a82e-4d00-b1c6-bf9fe1b7875d%2Ff99e4736-aa03-410b-8ba0-20a22e86d08d%2Fuq04b44_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the value of \( k \) that will make the function \( f(x) \) continuous everywhere.
\[
f(x) =
\begin{cases}
2x + k, & x \leq 2 \\
kx^2 - 5, & x > 2
\end{cases}
\]
Options:
- \( \frac{1}{8} \)
- 2
- such a \( k \) does not exist
- -3
- 3
[Explanation: The question presents a piecewise function \( f(x) \) with different expressions for \( x \leq 2 \) and \( x > 2 \). The task is to find a value of \( k \) that ensures the function is continuous across all values of \( x \).]
Expert Solution
Step 1
Given query is to find the the value of k.
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