This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Perez (nap563) HW02 Zheng (56555) 1 This printout should have 10 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find all functions g such that g ( x ) = 2 x 2 + 5 x + 1 x . 1. g ( x ) = x ( 2 x 2 + 5 x + 1 ) + C 2. g ( x ) = 2 x parenleftbigg 2 5 x 2 + 5 3 x 1 parenrightbigg + C 3. g ( x ) = x parenleftbigg 2 5 x 2 + 5 3 x + 1 parenrightbigg + C 4. g ( x ) = 2 x parenleftbigg 2 5 x 2 + 5 3 x + 1 parenrightbigg + C cor rect 5. g ( x ) = 2 x ( 2 x 2 + 5 x 1 ) + C 6. g ( x ) = 2 x ( 2 x 2 + 5 x + 1 ) + C Explanation: After division g ( x ) = 2 x 3 / 2 + 5 x 1 / 2 + x 1 / 2 , so we can now find an antiderivative of each term separately. But d dx parenleftbigg ax r r parenrightbigg = ax r 1 for all a and all r negationslash = 0. Thus 4 5 x 5 / 2 + 10 3 x 3 / 2 + 2 x 1 / 2 = 2 x parenleftbigg 2 5 x 2 + 5 3 x + 1 parenrightbigg is an antiderivative of g . Consequently, g ( x ) = 2 x parenleftbigg 2 5 x 2 + 5 3 x + 1 parenrightbigg + C with C an arbitrary constant. 002 10.0 points Determine f ( t ) when f ( t ) = 2(9 t 1) and f (1) = 5 , f (1) = 2 . 1. f ( t ) = 9 t 3 + 2 t 2 + 2 t 11 2. f ( t ) = 9 t 3 t 2 2 t 4 3. f ( t ) = 3 t 3 + t 2 + 2 t 4 4. f ( t ) = 3 t 3 t 2 2 t + 2 correct 5. f ( t ) = 9 t 3 2 t 2 2 t 3 6. f ( t ) = 3 t 3 + 2 t 2 + 2 t 5 Explanation: The most general antiderivative of f has the form f ( t ) = 9 t 2 2 t + C where C is an arbitrary constant. But if f (1) = 5, then f (1) = 9 2 + C = 5 , i.e., C = 2 . From this it follows that f ( t ) = 9 t 2 2 t 2 . The most general antiderivative of f is thus f ( t ) = 3 t 3 t 2 2 t + D , where D is an arbitrary constant. But if f (1) = 2, then f (1) = 3 1 2 + D = 2 , i.e., D = 2 . Consequently, f ( t ) = 3 t 3 t 2 2 t + 2 . Perez (nap563) HW02 Zheng (56555)...
View
Full
Document
 Spring '10
 ZHENG
 Math, Calculus

Click to edit the document details