MATH 265 Midterm: MATH 265 Iowa State m2Practice

• School: Iowa State University
• Department: Mathematics
• Course: MATH 265
• Professor: All

Document Summary

First practice midterm: find the directional derivative for the function f(x, y, z) = xz2 3xy + 2xyz 3x + 5y 17 from the point (2, 6, 3) in the direction of the origin, find. Y (0, 1) for f(x, y) = sin x + y2 cos x + y4 arctan(cid:0)x(y2 1)(cid:1) + ln(2esin x 1) sec(xy) tan(y 1). (hint: (cid:0) f/ x(cid:1)(a, b) = g (a) where g(x) = f(x, b), similarly for (cid:0) f/ y(cid:1)(a, b). : evaluate the following limits or show that they do not exist. Currently yops sell for three dollars each and zans sell for nine dollars each. By combining their production the new company en- joys economy of scope and is now able to produce y yops and z zans at a cost of 10 + 1. Determine how many yops and zans respec- tively should be made in order to maximize pro t.