chapter8Problems

chapter8Problems - Chapter 8 Exponential functions 8.1...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Page1 / 7

chapter8Problems - Chapter 8 Exponential functions 8.1...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online