exam2 - Granillo, Yvette Exam 2 Due: Nov 3 2005, 11:00 pm...

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Unformatted text preview: Granillo, Yvette Exam 2 Due: Nov 3 2005, 11:00 pm Inst: Edward Odell 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Find f ( x ) when f ( x ) = x + 1 x- 1 2 . 1. f ( x ) =- 6( x + 2) ( x- 1) 3 2. f ( x ) =- 4( x + 2) ( x- 1) 3 3. f ( x ) = 6( x- 2) ( x + 1) 3 4. f ( x ) = 6( x- 1) ( x + 1) 3 5. f ( x ) = 4( x- 1) ( x + 1) 3 6. f ( x ) =- 4( x + 1) ( x- 1) 3 correct Explanation: By the Chain and Quotient Rules, f ( x ) = 2 x + 1 x- 1 ( x- 1)- ( x + 1) ( x + 1) 2 . Consequently, f ( x ) =- 4( x + 1) ( x- 1) 3 . keywords: Stewart5e, derivative, quotient rule, chain rule 002 (part 1 of 1) 10 points Find the derivative of f when f ( x ) = tan x 5 + 2 sec x . 1. f ( x ) = sec 2 x 5 + 2 sec x tan x 2. f ( x ) = 5 + 2 cos x (5 cos x + 2) 2 correct 3. f ( x ) = 5 cos x + 2 (5 cos x + 2) 2 4. f ( x ) = 5 sin x + 2 cos x (5 cos x + 2) 2 5. f ( x ) = 5 sec x + 2 (5 + 2 sec x ) 2 6. f ( x ) =- sec 2 x (5 + 2 sec x tan x ) 2 Explanation: Now, tan x 5 + 2 sec x = sin x cos x 5 + 2 cos x = sin x 5 cos x + 2 . Thus f ( x ) = cos x 5 cos x + 2 + 5 sin 2 x (5 cos x + 2) 2 = cos x (5 cos x + 2) + 5 sin 2 x (5 cos x + 2) 2 . Consequently, f ( x ) = 5 + 2 cos x (5 cos x + 2) 2 , since cos 2 x + sin 2 x = 1. keywords: Stewart5e, 003 (part 1 of 1) 10 points Find the derivative of f when f ( x ) = 2 x sin 4 x + 1 2 cos 4 x. 1. f ( x ) = 8 x cos 4 x- 4 sin 4 x 2. f ( x ) =- 8 x cos 4 x Granillo, Yvette Exam 2 Due: Nov 3 2005, 11:00 pm Inst: Edward Odell 2 3. f ( x ) = 8 cos 4 x 4. f ( x ) = 8 x cos 4 x correct 5. f ( x ) = 8 x cos 4 x + 4 sin 4 x Explanation: Since d dx sin x = cos x, d dx cos x =- sin x, it follows that f ( x ) = 2 sin 4 x + 8 x cos 4 x- 2 sin 4 x. Consequently, f ( x ) = 8 x cos 4 x . keywords: Stewart5e, derivative, product rule, chain rule, trig functions 004 (part 1 of 1) 10 points Find the equation of the tangent line to the graph of 3 y 2- xy- 25 = 0 , at the point P = (10 , 5). 1. 4 y = x + 10 correct 2. 19 y = 5 x + 45 3. 4 y + x = 10 4. 19 y + 5 x = 45 5. 2 y = x Explanation: Differentiating implicitly with respect to x we see that 6 y dy dx- y- x dy dx = 0 , so dy dx = y 6 y- x . At P = (10 , 5), therefore, dy dx fl fl fl P = 1 4 . Thus by the point slope formula, the equation of the tangent line at P is given by y- 5 = 1 4 ( x- 10) . Consequently, 4 y = x + 10 . keywords: Stewart5e, 005 (part 1 of 1) 10 points The figure below shows the graphs of three functions: t One is the graph of the position function s of a car, one is its velocity v , and one is its acceleration a . Identify which graph goes with which function....
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exam2 - Granillo, Yvette Exam 2 Due: Nov 3 2005, 11:00 pm...

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