Study Guides (238,413)
Mathematics (129)
MATH 200 (4)
All (4)

Math_200_April_2006.pdf

9 Pages
122 Views

School
University of British Columbia
Department
Mathematics
Course
MATH 200
Professor
All
Semester
Winter

Description
April 11, 2006 MATH 200 Name Page 2 of 9 pages Marks [15] 1. If two resistors of resistanc1 Rd R 2re wired in parallel, then the resulting 1 1 1 resistance R satisﬁes the equation = + . Use the linear or diﬀerential R R 1 R 2 approximation to estimate the change in R 1f Rcreases from 2 to 1.9 ohms and R increases from 8 to hm.o 2 Continued on page 3 April 11, 2006 MATH 200 Name Page 3 of 9 pages [10] 2. Assume that the directional derivative of w = f(x,y,z)a tapoit P is a maximum in the direction o√ the vector 2i − j + k, and the value of the directional derivative in that direction is 3 6. (a) Find the gradient vector of w = f(x,y,z)a t P.[%] (b) Find the directional derivative of w = f(x,y,z)at P in the direction of the vector i + j[] Continued on page 4 April 11, 2006 MATH 200 Name Page 4 of 9 pages [10] 3. Use the Second Derivative Test to ﬁnd all values of the constant c for which the function z = x2 + cxy + y has a saddle point at (0,0). Continued on page 5 April 11, 2006 MATH 200 Name Page 5 of 9 pages [15] 4. Use the Method of Lagrange Multipliers (no credit will be given for any other method) to ﬁnd the radius of the base and the height of a right circular cylinder of maximum 2 2 2 volume which can be ﬁt inside the unit sphere x + y + z =1. Continued on page 6 April 11, 2006 MATH 200 Name
More Less

Related notes for MATH 200

OR

Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.