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MTH_133_FS11_SHAPIRO.huynhtr1.W-6.1

MTH_133_FS11_SHAPIRO.huynhtr1.W-6.1 - Trang Thien Vu Huynh...

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Trang Thien Vu Huynh MTH 133 FS11 SHAPIRO 011 WeBWorK assignment number W-6.1 is due : 09/10/2011 at 02:00am EDT. IMPORTANT: Check the due date information on the assignment page to see if this assignment has a reduced credit period before the due date. For help on any of these problems, please consult the MTH 133 WeBWorK Forum or start a new thread with your questions. The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are having trouble figuring out your error, you should consult the book, go to the Math Learning Center, or ask a fellow student, one of the TA’s or your professor for help. Don’t spend a lot of time guessing – it’s not very efficient or effective. Do not give decimal answers. Instead use fractions, pi, sqrt(2), etc.. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2 3 instead of 8, sin ( 3 * π / 2 ) instead of ( - 1 ) , e ln ( 2 ) instead of 2 , etc. Here’s the list of the functions which WeBWorK understands. For help entering answers, open DragMath in another window . c 2009-2010 WeBWorK Team, Department of Mathematics, Michigan State University 1. (1 pt) [Click to see a worked example.] Consider a solid which lies between planes perpendicular to the x-axis at length x = 0 and x = 5 . The cross-sections per- pendicular to the axis on the interval 0 x 5 are squares whose diagonals run from the parabola y = - x to the parabola y = x . What is the area of the cross-section at x ? A ( x ) = What is the volume of the solid ? V = SOLUTION The cross-section is a square so its area formula is s 2 , where s is a side of the square. From the Pythagorean theorem, we know that the square of the diagonal d is the sum of square of two sides so s = d 2 , where length of the diagonal is the distance between the curve y = x and y = - x . After A ( x ) has been computed, the volume is found by inte- grating the area A ( x ) from x = 0 to x = 5 . Correct Answers: 2*x 25 2. (1 pt) [Click to see a worked example.] Consider a solid which lies between planes perpendicular to the x-axis at length x = - 3 and x = 3 . The cross-sections per- pendicular to the x-axis between these planes are squares whose bases run from the semicircle y = - 9 - x 2 to the semicircle y = 9 - x 2 .
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