Homework 14-solutions

# Homework 14-solutions - wtm369 Homework 14 Helleloid(58250...

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wtm369 – Homework 14 – Helleloid – (58250) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points ±ind the value oF x when x = 3 4 p 3 log 3 2 P - 5 p 2 log 2 4 P . 1. x = - 1 4 2. x = 1 4 correct 3. x = - 7 24 4. x = 7 24 5. x = 1 3 Explanation: Since 3 log 3 x = x, 2 log 2 x = 1 x , we see that 3 log 3 2 = = 2 , while 2 log 2 4 = = 1 4 . Consequently, x = 3 2 - 5 4 = 1 4 . 002 10.0 points SimpliFy the expression f ( x ) = 8 6(log 8 e ) ln x as much as possible. 1. f ( x ) = x 6 correct 2. f ( x ) = x 48 3. f ( x ) = 6 x 4. f ( x ) = x 8 5. f ( x ) = e 49 Explanation: By the property oF inverse Functions, 8 log 8 y = y, e ln y = y . Consequently, f ( x ) = 8 6(log 8 e ) ln x = (8 log 8 e ) 6 ln x = e ln x 6 = x 6 . 003 10.0 points Rewrite the expression f ( x ) = ln ± x 2 - 4 x 4 ² using properties oF logarithms. 1. f ( x ) = ln( x 2 + 2) + 4 ln x 2. f ( x ) = ln( x + 2) - ln( x - 2) + 4 ln x 3. f ( x ) = ln( x + 2) - ln( x - 2) - 4 ln x 4. f ( x ) = ln( x + 2) + ln( x - 2) + 4 ln x 5. f ( x ) = ln( x + 2) + ln( x - 2) - 4 ln x correct 6. f ( x ) = ln( x 2 + 2) - 4 ln x Explanation: Since ln a + ln b = ln ab, r ln x = ln x r , ln a - ln b = ln p a b P

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wtm369 – Homework 14 – Helleloid – (58250) 2 and x 2 - 4 = ( x - 2)( x + 2) , we see that f ( x ) = ln( x 2 - 4) - ln x 4 = ln b ( x + 2)( x - 2) B - 4 ln x . Consequently, f ( x ) = ln( x + 2) + ln( x - 2) - 4 ln x . 004 10.0 points Which one of the following could be the graph of f ( x ) = log 3 | x - 4 | when a dashed line indicates an asymptote? 1. 2. cor- rect 3. 4. 5. 6. Explanation: Let’s Frst review some properties of ln x and ln( - x ). Since ln x is deFned only on (0 , ) and lim x 0 + ln x = -∞ , lim x →∞ ln x = ,
wtm369 – Homework 14 – Helleloid – (58250) 3 the graph of ln x has a vertical asymptote at x = 0 and so is given by But then ln( - x ) is deFned only on ( -∞ , 0) and has the properties lim x 0 - ln( - x ) = -∞ , lim x →−∞ ln( - x ) = , so its graph has a vertical asymptote at x = 0 and is given by Putting the two together we Fnally see that the graph of ln | x | has a vertical asymptote at x = 0 and so is given by Now the given function is f ( x ) = log 3 | x - 4 | . Its graph will have a vertical asymptote at

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## This note was uploaded on 12/04/2009 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas.

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Homework 14-solutions - wtm369 Homework 14 Helleloid(58250...

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