This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MATH 213: MIDTERM2 (FALL 2007) Name:__,_; _____________________________ __ Section: _________ __ TA: ________________ _ Score:
Problem 1 __________________________ __
Problem ________ _;___; _____ "I _____ __
Problem 3 ___________________________ __ Problem 4._______.__~______;_____ Problem 5._________r__________ Problem 6.____ ____ _; ________________ __ I Total:r___;_;_____~_____________ Instruction: Show all work. No work 2 no credit, even if you have a
correct answer. References and calculator are not allowed. Problem 1 (15 points): Consider the function z 2 f (cc, y) : x2y3.
(a) (10 points) Compute the partial derivatives g and g5. Then write
down the total differential dz. ' ' (b) (5 points) Use the total differential to ﬁnd the approximate value of
(2.01)2(0.99)3 Problem 2 (10 points): Let f (ac, y) = 2x3 +fy2 — Gary +27 Find all its critical
points. Determine if they are'points for relative maximum, relative minimum
or saddle points. ' Problem 3 (15 points): When a factory buys a: A machines and y B ma—
chines the‘productivity function is P(x, 3/) 2 3023;“. Machine A costs 3 thou
sand dollars each and machine B costs 2 thousand dollars each. Use La
grange’s method to ﬁnd the combination of A machines and B machines the factory can buy for 54 thousand dollars which will maximize the productivity
function. Problem 4 (10 points): Evaluate the double integral / / exsdxdy,
R Where R is the region in the xyplane bounded by x = 1, y = 0 and y = $2.
( Hint: choose a good order of integration. ) Problem 5 (10 points) Solve the following initial value problem: Problem 6 (10 points): Consider the initialvalue problem dy ’
. —— 2 1 — 2 ' 0 = 1'. Use Euler’s method with stepsize h = 0.1 to ﬁnd the approximate values of
I the solution at a: r: 0.1, 0.2 and 0.3. ...
View
Full
Document
This note was uploaded on 08/11/2008 for the course MATH 213 taught by Professor Chen,zhu during the Fall '07 term at University of Wisconsin.
 Fall '07
 CHEN,ZHU
 Differential Equations, Equations

Click to edit the document details