Practice test2b

Practice test2b - t t t y t v and its position when t = 1...

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Name 22 October 2009 Teaching Assistant Hour Test 2 Math 1501 J Andrew Instructions: 1. Closed book. 2. Show your work and explain your answers and reasoning. 3. Calculators may be used, but are by no means necessary. Pay particular attention to instruction 2. To receive credit, you must show your work. Unexplained answers, and answers not supported by the work you show, will not receive credit. 4. Express your answers in simplified form. 1. (25) a. Find the first and second derivatives of - = x t dt t e x F 0 2 ) sin( ) ( b. Evaluate i. ( 29 - dx x 1 3 ii. π 0 ) ( sin dx x iii. 2 0 ) cos( ) ( sin dx x x 2. (25) A package to be shipped by the United States Postal Service (USPS) must satisfy the condition "length + girth" no larger than 108 inches. Find the radius and length of the cylindrical mailing tube of maximal volume that may be shipped by USPS. Use the second derivative test to convince me that you've found a maximum. 3. (25) A particle moves on a y -axis in such a way that its velocity is given as a function of time t as 1 4 3 ) ( ' ) ( 2 + - = =
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Unformatted text preview: t t t y t v and its position when t = 1 is 5 ) 1 ( = y . a. On what interval(s) (of time t ) is y increasing? On what interval(s) is y decreasing? b. What is the position (value of y ) when t = 5? c. What is the particle's acceleration when t = 1? Name Page 2 of 3 Hour Test 2 Teaching Assistant 22 October 2009 4. a. Sketch the region that lies in the first quadrant and is bounded by the line x y + = 4 , the y-axis, and the parabola 2 2 x y + = . b. Calculate the area of the region described in part a . Name Page 3 of 3 Hour Test 2 Teaching Assistant 22 October 2009 ANSWERS 1. a. ) sin( ) ( ' 2 x e x F x-= , ( 29 ) cos( ) sin( 2 ) ( ' ' 2 x x e x F x +-=-b. i. C x x +-4 4 1 ii. 2 iii. 2 1 2. 3 108 = r , 3 108 = l , 216 3 108 ' '-= V is negative, so we have found a maximum. 3. a. Increasing on ) 3 1 , ( -and on ) , 1 ( . Decreasing on ) 1 , 3 1 ( b. 85 ) 5 ( = y c. 2 ) 1 ( ' ' = y 4. a. . b. 3 16 = A...
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Practice test2b - t t t y t v and its position when t = 1...

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