MATH 2153 Midterm: Math 2153 midterm-2-solutions

• School: Ohio State University
• Department: Mathematics
• Course: MATH 2153
• Professor: All

Document Summary

Practice midterm 2 math 2153: decide if the following statements are true or false and circle your answer. You do not need to justify your answers. (a) (1 point) if both partial derivatives fx and fy exist at (a, b) then f is di erentiable at (a, b). Solution: t: give examples of the following. Solution: f (x, y) = 0 (b) (2 points) give an example of a function f (x, y, z) for which the graph of z = sin(xy) is a level surface. F (x, y, z) = z sin(xy) (c) (2 points) give an example of a function f (x, y) with domain r2 for which fx(0, 0) exists but fy(0, 0) does not exist. Solution: f (x, y) = |y| (d) (2 points) sketch level curves for a function f (x, y) with four local maximuma and no local minima. Make sure to include enough level curves to illustrate these properties.