PILOT Problem Set 4.pdf - Pilot Problem set 4 week of Feb 21 ~ 1 Describe the image of the curve X(t =< 2 sin t 4 cos t t > 0 t 2 2 Find the terms up to

# PILOT Problem Set 4.pdf - Pilot Problem set 4 week of Feb...

• Homework Help
• 1

This preview shows page 1 out of 1 page.

Pilot Problem set 4, week of Feb. 21 1. Describe the image of the curve~X(t) =<2 sint,4 cost, t >, 0t2π. 2. Find the terms up to second order of the Taylor expansion of x 4 + x 2 y 2 - y 4 about the point (1,1). Verify your answer by finding (by direct computation) the exact Taylor expansion. 3. Find all the critical points of f ( x, y ) = x 3 + 3 xy 2 - 3 x 2 - 3 y 2 + 4 and test for relative max or min. 4. In R 3 , find the minimum distance from the origin to the surface Unformatted text preview: of the cone C = { ( x, y, z ) : z 2 = ( x-1) 2 + ( y-2) 2 } . Do not use Lagrange multipliers. 5. Redo problem 4 by the method of Lagrange multipliers. 6. Let ~ f ( t ) : R → R 3 be a vector function satisfying ~ f ( t ) = ~ f ( t ) , ~ f (0) = 2 &lt; 1 , 1 , 1 &gt; . Find ~ f ( t ). 1...
View Full Document

### 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

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes