math111_2006spring_prelim3sol - Math 111 Prelim 3 April 25,...

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Unformatted text preview: Math 111 Prelim 3 April 25, 2006 Name: Instructor: Section: INSTRUCTIONS READ THIS NOW This test has 10 problems on 10 pages worth a total of 100 points. Look over your test package right now . If you find any missing pages or problems please ask a proctor for another test booklet. Write your name, your instructors name, and your section number right now . Show your work. To receive full credit, your answers must be neatly written and logically organized. If you need more space, write on the back side of the preceding sheet, but be sure to label your work clearly. This is a 90 minute test. You are allowed to use your calculator and a 3 5 inch index card of notes. All other aids are prohibited. You DO NOT need to SIMPLIFY your answers. OFFICIAL USE ONLY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Total: Math 111 (Spring 2006) Prelim 3 (4/25/2006) 2 1. [16pts (4pts each)] (a) Evaluate integraldisplay [2 e x + 4 cos x ] dx = 2 e x + 4 sin x + C (b) Evaluate integraldisplay 2 1 4 + u 2 u 3 du = integraldisplay 2 1 4 u 3 + 1 u du =- 2 u 2 + ln | u | vextendsingle vextendsingle vextendsingle vextendsingle 2 1 =- 1 2 + ln 2- (- 2 + 0) = 3 2 + ln 2 CONTINUE TO NEXT PAGE Math 111 (Spring 2006) Prelim 3 (4/25/2006) 3 (c) Evaluate integraldisplay sin( )- 1 cos 2 ( ) d = integraldisplay sin( ) cos( ) 1 cos( )- 1 cos 2 ( ) d = integraldisplay tan( ) sec( )- sec 2 ( ) d = sec( )- tan( ) + C (d) Find the most general antiderivative of f ( x ) = 1 x cos( x )- ln( x ) sin( x ) . F ( x ) = cos x ln x + C CONTINUE TO NEXT PAGE Math 111 (Spring 2006) Prelim 3 (4/25/2006) 4 2. [8 pts] Find the derivative of h ( x ) = integraldisplay e x sin 3 t dt =- integraldisplay e x sin 3 t dt h ( x ) =- e x sin 3 ( e x ) 3. [8 pts] Given that integraldisplay x 1 2 f ( t ) dt = x 2 cos 2 x find f ( x ). d dx integraldisplay x 1 2 f ( t ) dt = d dx x 2 cos 2 x 2 f ( x ) =- 2 x 2 cos x sin x + 2 x cos 2 x 2 f ( x ) = 2( x cos 2 x- x 2 cos x sin x ) f ( x ) = x cos 2 x- x 2 cos x sin x CONTINUE TO NEXT PAGE Math 111 (Spring 2006) Prelim 3 (4/25/2006) 5 4. [7 pts] If w ( t ) is the rate of growth of a child in pounds per year, what does integraldisplay 10 5 w ( t ) dt represent?...
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math111_2006spring_prelim3sol - Math 111 Prelim 3 April 25,...

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