{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

271E3-F2003

# 271E3-F2003 - MATHEMATICS 271 TEST III FALL 2002 8(10 pts 1...

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATHEMATICS 271 TEST III FALL 2002 8 (10 pts) 1) Find 6—: at (m,y,z)=(2,1,—1) if w=p;an=—x+y+za q:m—y+z, andr=x+y+z. (10 pts) 2) If f(:z:,y,z) = y2 +zlnx ﬁnd a) Vf at (1,171)) b) the direction in which f changes most rapidly at (1,1,1), c) the equation of the tangent plane to y2 + zlnx = 1 at (1, 1, 1). (10 pts) 3) Find all maxima, minima, and points of inﬂection of f (:1), y) = x3 — y3 — 21:31 + 6. (10 pts) E)va1uate by reversing the order of integration. He My (10 pts) 5) Find the average value of f(ac, y) = ycos a: in the area bounded by y = O, y = sin :3, 0 S a: g 7r. (10 pts) 6) If f(:r,y) = ysinm ﬁnd a) The linear approximation near (0,0). b) The quadratic approximation near (0,0). c) An estimate of the error made if f is replaced by its quadratic approximation. Assume |Aac| < 10‘2 and |Ay| < 10—2. (10 pts) 7) Find the absolute maximum and minimum of f (51:, y) = x2 + my + y2 — 6:1: + 2 on {(117,y)|0 S A S 57 _3 S y S 0} (10 pts) 8) Find the largest product of the positive numbers 2:, y, and z if m + y + z2 = 16. (20 pts) 9) Set up but do not evaluate integrals for the following a) The area inside t = 2(1 + sin 0) and outside 7' = 1, b) I z (the moment of inertia with respect to the z~axis) of the tetrahedan with corners (0,0,0), (1,0,0), (0,2,0), and (0,0,2) if the density 6 = my. c) The volume between the cylinders 132 + y2 = 4 and :62 + y2 = 1 inside 3:2 + y2 + 22 = 9. d) The volume inside 2 = \/\$2 + :92 and m2 + 11/2 + 22 = 9. e) The area for the smaller part of the region cut from m2 + 4312 = 12 by a: = 4:92. ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern