chapter8Problems

# chapter8Problems - Chapter 8 Exponential functions 8.1...

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Unformatted text preview: Chapter 8 Exponential functions 8.1 Graph the following functions: (a) f ( x ) = x 2 e- x (b) f ( x ) = ln( x 2 + 3) (c) f ( x ) = ln( e 2 x ) 8.2 Express the following in terms of base e : (a) y = 3 x (b) y = 1 7 x (c) y = 15 x 2 +2 Express the following in terms of base 2: (d) y = 9 x (e) y = 8 x (f) y =- e x 2 +3 Express the following in terms of base 10: (g) y = 21 x (h) y = 1000- 10 x (i) y = 50 x 2- 1 v.2005.1 - September 4, 2009 1 Math 102 Problems Chapter 8 8.3 Compare the values of each pair of numbers (i.e. indicate which is larger): (a) 5 . 75 , 5 . 65 (b) 0 . 4- . 2 , . 4 . 2 (c) 1 . 001 2 , 1 . 001 3 (d) 0 . 999 1 . 5 , . 999 2 . 3 8.4 Rewrite each of the following equations in logarithmic form: (a) 3 4 = 81 (b) 3- 2 = 1 9 (c) 27- 1 3 = 1 3 8.5 Solve the following equations for x : (a) ln x = 2 ln a + 3 ln b (b) log a x = log a b- 2 3 log a c 8.6 Reflections and transformations What is the relationship between the graph of y = 3 x and the graph of each of the following functions? (a) y =- 3 x (b) y = 3- x (c) y = 3 1- x (d) y = 3 | x | (e) y = 2 · 3 x (e) y = log 3 x 8.7 Solve the following equations for x : (a) e 3- 2 x = 5 (b) ln(3 x- 1) = 4 (c) ln(ln( x )) = 2 (d) e ax = Ce bx , where a negationslash = b and C > 0. v.2005.1 - September 4, 2009 2 Math 102 Problems Chapter 8 8.8 Find the first derivative for each of the following functions: (a) y = ln(2 x + 3) 3 (b) y = ln 3 (2 x + 3) (c) y = ln(cos 1 2 x ) (d) y = log a ( x 3- 2 x ) (Hint : d dx (log a x ) = 1 x ln a ) (e) y = e 3 x 2 (f) y = a- 1 2 x (g) y = x 3 · 2 x (h) y = e e x (i) y = e t- e- t e t + e- t 8.9 Find the maximum and minimum points as well as all inflection points of the following functions: (a) f ( x ) = x ( x 2- 4) (b) f ( x ) = x 3- ln( x ) , x > (c) f ( x ) = xe- x (d) f ( x ) = 1 1- x + 1 1+ x ,- 1 < x < 1 (e) f ( x ) = x- 3 3 √ x (f) f ( x ) = e- 2 x- e- x...
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## This note was uploaded on 05/19/2011 for the course MATH 102 Math 102 taught by Professor Allard during the Winter '09 term at UBC.

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chapter8Problems - Chapter 8 Exponential functions 8.1...

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