Consider the piecewise defined function Find the values of a and b that make the following function continuous. g(x) x² + ax+ 36 -x²+5a if x < 2 -{ if x > 2 Use the limit definition of the derivative to determine all possible values of a and b that make g into a differentiable function at x =2. What is the value of b? (You do not need to enter the value of a.) Enter your answer as a decimal. Round to three decimal places (as needed).
Consider the piecewise defined function Find the values of a and b that make the following function continuous. g(x) x² + ax+ 36 -x²+5a if x < 2 -{ if x > 2 Use the limit definition of the derivative to determine all possible values of a and b that make g into a differentiable function at x =2. What is the value of b? (You do not need to enter the value of a.) Enter your answer as a decimal. Round to three decimal places (as needed).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Consider the piecewise defined function. Find the values of \( a \) and \( b \) that make the following function continuous.
\[
g(x) =
\begin{cases}
x^2 + ax + 3b & \text{if } x \geq 2 \\
-x^2 + 5a & \text{if } x < 2
\end{cases}
\]
Use the limit definition of the derivative to determine all possible values of \( a \) and \( b \) that make \( g \) into a differentiable function at \( x = 2 \).
What is the value of \( b \)? (You do not need to enter the value of \( a \).)
Enter your answer as a decimal. Round to three decimal places (as needed).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f609e33-8915-43d7-970a-e560ca4358ea%2F002f1412-8695-474b-bbc8-8d5113a7e014%2F06nl9m_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the piecewise defined function. Find the values of \( a \) and \( b \) that make the following function continuous.
\[
g(x) =
\begin{cases}
x^2 + ax + 3b & \text{if } x \geq 2 \\
-x^2 + 5a & \text{if } x < 2
\end{cases}
\]
Use the limit definition of the derivative to determine all possible values of \( a \) and \( b \) that make \( g \) into a differentiable function at \( x = 2 \).
What is the value of \( b \)? (You do not need to enter the value of \( a \).)
Enter your answer as a decimal. Round to three decimal places (as needed).
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