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**Unformatted text preview: **Chapter 3 Application of derivatives. (Review) Stephen Suen Chapter 4 Exponential and logarithmic functions – p. 1/10 4.1 Exponential functions Chapter 4 Exponential and logarithmic functions – p. 2/10 4.1 Exponential functions A . Loosely speaking, an exponential function (with base b , where b > and b negationslash = 1 ) is a function of the form f ( x ) = b x . Chapter 4 Exponential and logarithmic functions – p. 2/10 4.1 Exponential functions A . Loosely speaking, an exponential function (with base b , where b > and b negationslash = 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 . Chapter 4 Exponential and logarithmic functions – p. 2/10 4.1 Exponential functions A . Loosely speaking, an exponential function (with base b , where b > and b negationslash = 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 = ∞ . Chapter 4 Exponential and logarithmic functions – p. 2/10 4.1 Exponential functions A . Loosely speaking, an exponential function (with base b , where b > and b negationslash = 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 .” Chapter 4 Exponential and logarithmic functions – p. 2/10 4.1 Exponential functions A . Loosely speaking, an exponential function (with base b , where b > and b negationslash = 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, . 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 4.1.1 Graphs of exponential functions Chapter 4 Exponential and logarithmic functions – p. 3/10 4.1.1 Graphs of exponential functions Note that 2 = 3 = 1 , and that the graphs of y = 2 x , y = 2- x...

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