{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

S01_First_Midterm_Makeup-G.Bergman

S01_First_Midterm_Makeup-G.Bergman - function on the...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
l0/04/2O0I THU 16:14 FAX 6434990 GeorgeM. Bergman 959 Evans MOFFITT LIBRARY Spring 2001, Math 53M First Midterm - Make-up Exam @ oor 23 February,2O0l l0:10-11:00AM 1. (a) (54 points, 9 points apiece) Find the following. If an expression is undefined, say so. dy,/dx, where ,r= 2sin ("t), y = 5cos(et). Express your answer as a function of t. (b) The length of the space curve given by the parametric equations x = 2 "r, y = "2r, z=t (-1 <l(+1). (") tifl,,-'(o,o) (lxl+2)/( lrl+7). (d) Thc equation of the plane tangent to the surface ,= (*2 +y)% at the point where x=3, !=7. a . \ L t") #En f?yz) where / is a clifferentiable function. @xpress your answer in terms of / and its derivatives.) * "-"j+ (tan t)k))dt (where i, j and k are the standard basis vectors 2. (34 points) (a) (20 points) Let f be a positive continuous real-valued function on the
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: function on the interval f-n/4, n/4'1. L'et A denote the area between the curve whose expression in polar coordinates is r = f(o) (-n/4 < o < n/4) andthe two lines o = -n/4 and 0 = n/4. Let B denote the area between the curve whose expression in polar coordinates is r=f(0/2) (-n/2<o<n/2) andtheverticalaxis a=!n/2. showthat B=zA. You may assume area formulas given in Stewart. (b) (14 points) Find the area between the y-axis and the curve whose expression in polar coordinates is r = sec O/2. You may use the result of part (a) whether or not you have proved it; or you may use any other method that gives the correct answer. 3. (12 points) Find equations in Canesian (i.e., (x,y, z)) and spherical coordinates for the surface described in cylindrical coordinates by the equation y2 = 72 + r. {D [i<tz x 1t2i in IR')....
View Full Document

{[ 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