HW14-solutions - white (taw933) HW14 ben-zvi (55600) 1 This...

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Unformatted text preview: white (taw933) HW14 ben-zvi (55600) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find the derivative of f when f ( ) = ln (cos 3 ) . 1. f ( ) =- 1 sin 3 2. f ( ) =- 3 cot 3 3. f ( ) = 3 cos 3 4. f ( ) = cot 3 5. f ( ) =- 3 tan3 correct 6. f ( ) = 3 tan3 Explanation: By the Chain Rule, f ( ) = 1 cos(3 ) d d (cos 3 ) =- 3 sin 3 cos 3 . Consequently, f ( ) =- 3 tan 3 . 002 10.0 points Find the slope of the line tangent to the graph of ln( xy )- 2 x = 0 at the point where x = 1. 1. slope = 1 2 e 2 2. slope = e 2 correct 3. slope =- 1 2 e 2 4. slope = e 2 5. slope =- e 2 6. slope =- 1 2 e 2 Explanation: Differentiating implicitly with respect to x we see that 1 xy parenleftBig y + x dy dx parenrightBig- 2 = 0 , in which case dy dx =- y (1- 2 x ) x =- e 2 x (1- 2 x ) x 2 because, by exponentiation, y = e 2 x x . Consequently, at x = 1, slope = dy dx vextendsingle vextendsingle vextendsingle x =1 = e 2 . 003 10.0 points Find the derivative of f ( t ) = 1 + ln t 4- ln t . 1. f ( t ) = 5 t (4- ln t ) 2 correct 2. f ( t ) = 4 t (1 + ln t ) 2 3. f ( t ) =- 4 ln t t (1 + ln t ) 2 4. f ( t ) =- 5 t (4- ln t ) 2 5. f ( t ) = 4 ln t (1 + ln t ) 2 6. f ( t ) =- 5 (4- ln t ) 2 white (taw933) HW14 ben-zvi (55600) 2 Explanation: By the Quotient Rule, f ( t ) = (4- ln t )(1 /t ) + (1 + ln t )(1 /t ) (4- ln t ) 2 = (4- ln t ) + (1 + ln t ) t (4- ln t ) 2 . Consequently, f ( t ) = 5 t (4- ln t ) 2 . 004 10.0 points Find the derivative of f when f ( x ) = 2 ln( x- radicalbig x 2- 3) , ( x > 3) . 1. f ( x ) =- 4 x 2- 3 2. f ( x ) = 4 x 2- 3 3. f ( x ) = 2 x 2- 3 4. f ( x ) =- 2 x 2- 3 correct 5. f ( x ) = 1 x 2- 3 6. f ( x ) =- 1 x 2- 3 Explanation: By the Chain Rule f ( x ) = 2 x- x 2- 3 parenleftBig 1- x x 2- 3 parenrightBig =- 2 x 2- 3 . 005 10.0 points Determine f ( x ) when f ( x ) = e (3 ln( x 5 )) . 1. f ( x ) = 1 x e 3 ln( x 5 ) 2. f ( x ) = 15 x 14 correct 3. f ( x ) = 15(ln x ) e 3 ln( x 5 ) 4. f ( x ) = e 15 /x 5. f ( x ) = 14 x 15 6. f ( x ) = 3 x 2 e 3 ln( x 5 ) Explanation: Since r ln x = ln x r , e ln x = x , we see that...
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HW14-solutions - white (taw933) HW14 ben-zvi (55600) 1 This...

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