m408k_practicetest2_solutions

m408k_practicetest2_solutions - Create assignment 59515...

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Create assignment, 59515, Practice 2, Oct 27 at 12:28 pm 1 This print-out should have 30 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. The due time is Central time. CalC3f01c 49:04, calculus3, multiple choice, > 1 min, wording-variable. 001 ±ind the derivative oF f ( x ) = 3 x sin 4 x + 3 4 cos 4 x. 1. f 0 ( x ) = 12 x cos 4 x correct 2. f 0 ( x ) = 12 x cos 4 x + 6 sin 4 x 3. f 0 ( x ) = - 12 x cos 4 x 4. f 0 ( x ) = 12 x cos 4 x - 6 sin 4 x 5. f 0 ( x ) = 12 cos 4 x Explanation: Since d dx sin x = cos x, d dx cos x = - sin x, it Follows that f 0 ( x ) = 3 sin 4 x + 12 x cos 4 x - 3 sin 4 x. Consequently, f 0 ( x ) = 12 x cos 4 x . keywords: derivative, product rule, chain rule, trig Functions CalC3f01d 49:04, calculus3, multiple choice, > 1 min, wording-variable. 002 Determine f 0 ( x ) when f ( x ) = 2 sin 3 x - 3 cos 2 x. 1. f 0 ( x ) = 6(cos 3 x + sin 2 x ) correct 2. f 0 ( x ) = - 6(sin 2 x + cos 3 x ) 3. f 0 ( x ) = 2 cos 3 x - 3 sin 2 x 4. f 0 ( x ) = 2 cos 3 x + 3 cos 2 x 5. f 0 ( x ) = - (3 sin 2 x + 2 cos 3 x ) 6. f 0 ( x ) = 6(cos 3 x - sin 2 x ) Explanation: Since d dx sin x = cos x, d dx cos x = - sin x, the Chain Rule ensures that f 0 ( x ) = 6(cos 3 x + sin 2 x ) . keywords: derivative, chain rule, trig Function CalC3f02a 49:04, calculus3, multiple choice, > 1 min, wording-variable. 003 ±ind f 0 ( x ) when f ( x ) = x + 1 x - 1 · 2 . 1. f 0 ( x ) = - 4( x + 1) ( x - 1) 3 correct 2. f 0 ( x ) = 6( x - 2) ( x + 1) 3 3. f 0 ( x ) = - 6( x + 2) ( x - 1) 3 4. f 0 ( x ) = - 4( x + 2) ( x - 1) 3 5. f 0 ( x ) = 6( x - 1) ( x + 1) 3
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Create assignment, 59515, Practice 2, Oct 27 at 12:28 pm 2 6. f 0 ( x ) = 4( x - 1) ( x + 1) 3 Explanation: By the Chain and Quotient Rules, f 0 ( x ) = 2 x + 1 x - 1 · ( x - 1) - ( x + 1) ( x + 1) 2 . Consequently, f 0 ( x ) = - 4( x + 1) ( x - 1) 3 . keywords: derivative, quotient rule, chain rule CalC3f06a 49:04, calculus3, multiple choice, < 1 min, wording-variable. 004 Find the derivative of y when y = 2 sin x - 6 x cos x. 1. y 0 = 3 sin x - 2 cos x x · correct 2. y 0 = sin x + 2 cos x x · 3. y 0 = 3 sin x - 4 cos x x · 4. y 0 = sin x + 4 sin x x · 5. y 0 = 3 cos x - 4 sin x x · 6. y 0 = cos x + 2 sin x x · Explanation: By the Product and Chain Rules, y 0 = cos x x - 3 cos x x · + 3 x sin x x · . Consequently, y 0 = 3 sin x - 2 cos x x · . keywords: derivative, trig function, square root CalC3f25a 49:04, calculus3, multiple choice, < 1 min, wording-variable. 005 Find the derivative of f when f ( x ) = ( x 2 + 4) 1 / 4 ( x + 6) 1 / 2 . 1. f 0 ( x ) = 3 x - 2 2( x 2 + 4) 3 / 4 ( x + 6) 3 / 2 2. f 0 ( x ) = 3 x - 2 ( x 2 + 4) 3 / 4 ( x + 6) 3 / 2 correct 3. f 0 ( x ) = 3 x + 2 2( x 2 + 4) 3 / 4 ( x + 6) 3 / 2 4. f 0 ( x ) = 3 x + 2 ( x 2 + 4) 1 / 4 ( x + 6) 3 / 2 5. f 0 ( x ) = 3 x + 2 2( x 2 + 4) 3 / 4 ( x + 6) 1 / 2 6. f 0 ( x ) = 3 x - 2 ( x 2 + 4) 1 / 4 ( x + 6) 1 / 2 Explanation:
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This note was uploaded on 03/18/2008 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas.

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m408k_practicetest2_solutions - Create assignment 59515...

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