advertisement

Math 2720: Multiviariable Calculus Homework #3 Due Tuesday, January 20 In class, we talked about the graphs of degree one functions like p(x, y) = 3x + 2y + 1, and found that the graphs are planes. Problem 1 Consider the function f (x, y) = x2 y + y 2 x. (a) Determine the slope of f in the x-direction at (1, 1). (b) Determine the slope of f in the y-direction at (1, 1). (c) Find a degree one function p(x, y) with the same x-direction slope and y-direction slope as f at the point (1, 1). (d) If necessary, modify your answer to (c) so that it is also true that p(1, 1) = f (1, 1). You have found the tangent plane to the graph of f at (1, 1). Problem 2 Consider the following 2-variable trajectory problem: You launch a ball in R2 from the origin at angle θ and velocity v; where does it cross the x-axis? Solving this problem gives you a function S(θ, v) = the solution to the problem . (a) Find a formula for the function S. (b) Find the tangent plane to the graph of X over the point θ = v = 12 . π , 6 (c) Find the tangent plane to the graph of X over the point θ = v = 32 . π , 4