MATH 100 Midterm: MATH 100 KSU Spring2012SCAExam1answerkey

• School: Kansas State University
• Department: Mathematics
• Course: MATH 100
• Professor: All

Document Summary

Answers which are illeg- ible for the grader cannot be given credit: show your work. Except for problems 1-2, we need to see details of your computation: no notes, books, calculators, computers, or other electronic aids can be allowed, you have 90 minutes time to complete your work. Problem 1) true/false questions (20 points), no justi cations needed. The directional derivative d~vf is a vector perpendicular to ~v. The directional derivative is a scalar, not a vector. Using linearization of f (x, y) = xy we can estimate f (0. 9, 1. 2) 1 0. 1 + L(x, y) = 1 1 0. 1 + 1 0. 2. Given a curve ~r(t) on a surface g(x, y, z) = 1, then d dt g(~r(t)) = 0. This fact is used in the proof that level surfaces are perpendicular to gradients. Dh0, 1if (0, 0) = 0. such that f (0, 0) = h2, 1i.