Is on the edge of the shadow how far above the x axis

This preview shows page 2 - 3 out of 4 pages.

is on the edge of the shadow, how far above the x -axis is the lamp located? units above the x -axis. Answer(s) submitted: inf (incorrect) Correct Answers: 2 9. (1 point) Use implicit differentiation to find an equation of the tangent line to the curve sin ( x + y ) = 4 x - 4 y at the point ( π , π ) . Tangent Line Equation: Answer(s) submitted: y-pi=3/5(x-pi ) (correct) Correct Answers: y-0.6*x = 1.25664 10. (1 point) If x 2 + y 3 - 2 xy 2 = 33, find dy / dx in terms of x and y . dy dx = Using your answer for dy / dx , fill in the following table of approximate y -values of points on the curve near x = 1 , y = 4. 0.96 0.98 1.02 1.04 Finally, find the y -value for x = 0 . 96 by substituting x = 0 . 96 in the original equation and solving for y using a computer or calculator. y ( 0 . 96 ) How large (in magnitude) is the difference between your esti- mate for y ( 0 . 96 ) using dy / dx and your solution with a computer or calculator? Solution: SOLUTION Implicitly differentiating the equation yields 2 x + 3 y 2 dy dx - 2 y 2 - 4 xy dy dx = 0, so that dy dx = 2 y 2 - 2 x 3 y 2 - 4 xy . We can approximate the curve near x = 1, y = 4 by its tan- gent line. The tangent line will have slope 2 ( 4 ) 2 - 2 ( 1 ) 3 ( 4 ) 2 - 4 ( 1 )( 4 ) 0 . 938. Thus its equation is y 4 + 0 . 938 ( x - 1 ) . Using the y -values of the tangent line to approximate the y - values of the curve, we get y ( 0 . 96 ) 3 . 9625, y ( 0 . 98 ) 3 . 9813, y ( 1 . 02 ) 4 . 0188, and y ( 1 . 04 ) 4 . 0375. When x = 0 . 96, we get the equation ( 0 . 96 ) 2 + y 3 - 2 ( 0 . 96 ) y 2 = 33, whose solution by numerical methods (for ex- ample, using a calculator) is 3.96276. The difference between 3.96276 and the estimate is just | 3 . 96276 - 3 . 9625 | = 0 . 0003. Answer(s) submitted: (2(yˆ2-x))/(y(3y-4x)) 15/16 (score 0.1428571492433548) Correct Answers: [2*yˆ2-2*xˆ(2-1)]/(3*yˆ2-2*2*x*y) 4+0.9375*(0.96-1) 4+0.9375*(0.98-1) 4+0.9375*(1.02-1) 4+0.9375*(1.04-1) 3.96276
Image of page 2

Subscribe to view the full document.

Image of page 3
  • Fall '13
  • DrSulllivan
  • Mathematical analysis, Logarithm, 6x-2, Denise Mbenza, Find y0

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern