# hw7so - Create assignment, 57321, Homework 6, Mar 22 at...

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Unformatted text preview: Create assignment, 57321, Homework 6, Mar 22 at 4:56 pm 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. CalC4j00Ex2 51:01, calculus3, multiple choice, > 1 min, wording-variable. 001 Find all functions g such that g ( x ) = 3 x 2 + 4 x + 1 √ x . 1. g ( x ) = 2 √ x µ 3 5 x 2 + 4 3 x + 1 ¶ + C cor- rect 2. g ( x ) = √ x µ 3 5 x 2 + 4 3 x + 1 ¶ + C 3. g ( x ) = 2 √ x µ 3 5 x 2 + 4 3 x- 1 ¶ + C 4. g ( x ) = 2 √ x ( 3 x 2 + 4 x + 1 ) + C 5. g ( x ) = √ x ( 3 x 2 + 4 x + 1 ) + C 6. g ( x ) = 2 √ x ( 3 x 2 + 4 x- 1 ) + C Explanation: After division g ( x ) = 3 x 3 / 2 + 4 x 1 / 2 + x- 1 / 2 , so we can now find an antiderivative of each term separately. But d dx µ ax r r ¶ = ax r- 1 for all a and all r 6 = 0. Thus 6 5 x 5 / 2 + 8 3 x 3 / 2 + 2 x 1 / 2 = 2 √ x µ 3 5 x 2 + 4 3 x + 1 ¶ is an antiderivative of g . Consequently, g ( x ) = 2 √ x µ 3 5 x 2 + 4 3 x + 1 ¶ + C with C an arbitrary constant. keywords: antiderivative, power functions CalC4j00Ex4 51:01, calculus3, multiple choice, > 1 min, wording-variable. 002 Stewart Section 4.10, Example, 4 page 302 Determine f ( t ) when f 00 ( t ) = 2(9 t + 1) and f (1) = 4 , f (1) = 6 . 1. f ( t ) = 3 t 3 + t 2- 7 t + 9 correct 2. f ( t ) = 3 t 3- 2 t 2 + 7 t- 2 3. f ( t ) = 9 t 3 + t 2- 7 t + 3 4. f ( t ) = 3 t 3- t 2 + 7 t- 3 5. f ( t ) = 9 t 3 + 2 t 2- 7 t + 2 6. f ( t ) = 9 t 3- 2 t 2 + 7 t- 8 Explanation: The most general anti-derivative of f 00 has the form f ( t ) = 9 t 2 + 2 t + C where C is an arbitrary constant. But if f (1) = 4, then f (1) = 9 + 2 + C = 4 , i.e., C =- 7 . From this it follows that f ( t ) = 9 t 2 + 2 t- 7 . Create assignment, 57321, Homework 6, Mar 22 at 4:56 pm 2 The most general anti-derivative of f is thus f ( t ) = 3 t 3 + t 2- 7 t + D , where D is an arbitrary constant. But if f (1) = 6, then f (1) = 3 + 1- 7 + D = 6 , i.e., D = 9 . Consequently, f ( t ) = 3 t 3 + t 2- 7 t + 9 . keywords: antiderivatives, second order derivatives, particular values CalC4j14s 51:01, calculus3, multiple choice, > 1 min, normal. 003 Find the most general anti-derivative of the function f ( x ) = 5 cos x- 3 sin x. 1. F ( x ) = 5 sin x + 3 cos x + C correct 2. F ( x ) = 5 cos x + 3 sin x + C 3. F ( x ) =- 5 sin x + 3 cos x + C 4. F ( x ) =- 5 cos x + 3 sin x + C 5. none of these Explanation: Since d dx sin x = cos x, d dx cos x =- sin x, we see immediately that the most general anti-derivative of f ( x ) = 5 cos x- 3 sin x is the function F ( x ) = 5 sin x + 3 cos x + C with C an arbitrary constant. keywords: antiderivative, trig function CalC4j29s 51:01, calculus3, multiple choice, > 1 min, wording-variable....
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## This note was uploaded on 03/20/2008 for the course M 408c taught by Professor Mcadam during the Spring '06 term at University of Texas.

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hw7so - Create assignment, 57321, Homework 6, Mar 22 at...

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