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Unformatted text preview: jiwani (amj566) Homework13 Fouli (58395) 1 This printout should have 23 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find the larger solution of the exponential equation 3 x 2 = 9 x +4 . 1. none of these 2. x = 4 3. x = 2 4. x = 2 5. x = 4 correct Explanation: By properties of exponents, 9 x +4 = 3 2 x +8 . Thus the given equation can be rewritten as 3 x 2 = 3 2 x +8 , which after equating exponents becomes x 2 = 2 x + 8 . This equation factors as ( x 4)( x + 2) = 0 , and so its solutions are x = 4 , 2. Hence the larger solution of the given equation is x = 4 . 002 10.0 points Which function has 2 4 2 4 2 4 2 4 as its graph? 1. f ( x ) = 2 x 1 3 2. f ( x ) = 3 x 2 3. f ( x ) = 2 2 x 1 4. f ( x ) = 2 3 x correct 5. f ( x ) = 3 x 3 6. f ( x ) = 2 x 1 2 Explanation: The given graph has the property that lim x f ( x ) = 2 . But lim x 2 x = 0 = lim x 3 x , while lim x 2 x = 0 = lim x 3 x , so f ( x ) must be one of 2 3 x , 2 2 x 1 . On the other hand, the yintercept of the given graph is at y = 1. Consequently, the graph is that of f ( x ) = 2 3 x . 003 10.0 points jiwani (amj566) Homework13 Fouli (58395) 2 Find the value of lim x parenleftbigg 4 e 2 x 3 e 2 x 3 e 2 x + e 2 x parenrightbigg . 1. limit = 1 4 2. limit = 1 4 3. limit = 3 4 4. limit = 3 4 5. limit = 4 3 correct 6. limit = 4 3 Explanation: After division we see that 4 e 2 x 3 e 2 x 3 e 2 x + e 2 x = 4 3 e 4 x 3 + e 4 x . On the other hand, lim x e ax = 0 for all a > 0. But then by properties of limits, lim x 4 3 e 4 x 3 + e 4 x = 4 3 . Consequently, limit = 4 3 . 004 10.0 points Determine f ( x ) when f ( x ) = e 4 x +3 . 1. f ( x ) = 4 e 4 x +3 4 x + 3 2. f ( x ) = 2 e 4 x +3 4 x + 3 3. f ( x ) = 4 e 4 x +3 4. f ( x ) = 2 e 4 x +3 4 x + 3 correct 5. f ( x ) = 1 2 e 4 x +3 4 x + 3 Explanation: By the chain rule f ( x ) = e 4 x +3 parenleftbigg d dx 4 x + 3 parenrightbigg = 2 e 4 x +3 4 x + 3 . 005 10.0 points Find f ( x ) when f ( x ) = e x cos( e x ) sin( e x ) . 1. f ( x ) = e 2 x sin( e x ) 2. f ( x ) = e x cos( e x ) 3. f ( x ) = e x sin( e x ) 4. f ( x ) = e 2 x cos( e x ) 5. f ( x ) = e 2 x sin( e x ) correct 6. f ( x ) = e x cos( e x ) 7. f ( x ) = e 2 x cos( e x ) 8. f ( x ) = e x sin( e x ) Explanation: By the Chain Rule, f ( x ) = e x cos( e x ) e x cos( e x ) e 2 x sin( e x ) . jiwani (amj566) Homework13 Fouli (58395) 3 Consequently, f ( x ) = e 2 x sin( e x ) ....
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 Spring '11
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