Exponential Functions

Exponential Functions - Exponential Functions:...

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Unformatted text preview: Exponential Functions: Differentiation & Integration Integration Section 5.4 Defn. of the Natural Exponential Function Exponential The inverse of the natural logarithmic function f(x) = ln x is called the natural exponential function : f –1 (x) = ex y = ex iff x = ln y f –1(x) = ex f(x) = ln x ln(ex) eln x ln =x =x e=1 Operations with Exponential Functions Functions 1. e e =e ab a a +b e a −b =e b e Properties of the Natural Exponential Function Exponential 1. The domain of f(x) = ex is ( − ∞ , ∞). 2. The function f(x) = ex is continuous, increasing, and one-to-one on its entire domain. x 3. The graph of f(x) = e is concave upward on its entire domain. lim e = 0 and lim e = ∞ x x → −∞ x x →∞ The Derivative of the Natural Exponential Function Exponential Let u be a differentiable function of x. 1. d e x = e x dx 2. du u du e =e dx dx Integration Rules for Exponential Functions Exponential Let u be a differentiable function of x. x x 1. e dx = e + c 2. ∫ e du = e ∫ u u +c Joke Time Joke How can you stop a skunk from smelling? Hold its nose Why do golfers wear 2 pairs of pants? In case they get a hole in one ...
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This note was uploaded on 12/01/2011 for the course MATH 112 taught by Professor Jarvis during the Fall '08 term at BYU.

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Exponential Functions - Exponential Functions:...

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