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Section 5.4
Exponential Functions – Differentiation and Integration
The inverse of the natural log function is 𝑓 𝑥 = 𝑒𝑥
-3 -2 -1 1 2 3
-3
-2
-1
1
2
x
y
Ex1: Solve 17 xe
Ex2: Find the relative extrema of ( ) xf x xe
Ex3: Integrate
a) b) 3 1xe dx
2
5 xxe dx
c) d)
1
2
xedx
xcos(sin )( )xx e dx
Ex4a: 1
0
xe dx
1
1
x
y
Ex4b: 1
01
x
x
edx
e
1
1
x
y
Ex4c: 0
1
cos( )x xe e dx
-1
1
x
y
Homework
• p. 359 # 37, 38, 39-59 odd, 99-123 eoo
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