# R4ps - Chapter 3 Application of derivatives(Review Stephen...

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Chapter 3 Application of derivatives. (Review) Stephen Suen Chapter 4 Exponential and logarithmic functions – p. 1/10

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4.1 Exponential functions A . Loosely speaking, an exponential function (with base b , where b > 0 and b n = 1 ) is a function of the form f ( x ) = b x . B . When b > 1 , we have lim x →∞ b x = lim x →-∞ b - x = , lim x →-∞ b x = lim x →∞ b - x = 0 . C . When b < 1 , we have lim x →∞ b x = lim x →-∞ b - x = 0 , lim x →-∞ b x = lim x →∞ b - x = . D . Note that 2 x is much bigger than x 2 when x → ∞ . We say that exponential functions y = b x , where b > 1 , exhibit exponential growth .” Similarly, 0 . 5 x = 1 2 x , decreases to 0 as x → ∞ , and we say that the exponential function y = b x , when b < 1 , exhibits “ exponential decay .” Chapter 4 Exponential and logarithmic functions – p. 2/10
Note that 2 0 = 3 0 = 1 , and that the graphs of y = 2 x , y = 2 - x are mirror images of each about the y -axis. Chapter 4 Exponential and logarithmic functions – p. 3/10

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## This note was uploaded on 01/02/2012 for the course MAC 2233 taught by Professor Danielyan during the Fall '08 term at University of South Florida.

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R4ps - Chapter 3 Application of derivatives(Review Stephen...

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