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
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Consider the piecewise defined function Find the values
of a and b that make the following function continuous.
g(x)
x² + ax+
36
{
if x > 2
-x²+5a 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).
Transcribed Image Text:Consider the piecewise defined function Find the values of a and b that make the following function continuous. g(x) x² + ax+ 36 { if x > 2 -x²+5a 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).
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