# Dwight Wu MATH 230 Written HW 5

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HOMEWORK QUESTIONS of the following functions is a solution to 1. The Laplace equation is defined as UT + Wy = 0. Determine whether each the Laplace Uny =2 Use + Uhy = O NOT a solution 2+2=0
2. Use the following applet to answer the questions that follow (clickable link) - Contour f(x, y) = 12 - y ? . Do not function The given function should be change (a) Determine Vf (r, y). (b) Calculate Vf(-2, -2). (c) Find the unit vector in the direction of fastest increase at the point (-2. -2). How do you know it is the direction of fastest (d) Sketch this unit vector on the contour map and provide that sketch ill your answer below. a. IF MIN= (5%, SI=K22 Ten , Nosi WE KEA Because one of the gradient Theorems Sate tort the diretion of fastest rate of increase of S at (2,-2) ¡ S where VS -2,2) point to 01 and f. sketch of directional derivative from 2e. unity To
(e) Let V = (3, 2). Calculate Du f (2, 1). (f) Sketch this on the contour map. (g) Provide an interpretation of your answers to the previous two parts. In other words, explain what the answers to (e) and (f) mean. e. D, \$ (2,1) = VS (2,1) • U (3,2) W3, J3/ 3 V5(21) =<22), 20) =14, 2) The Answers to 13 Parts e and f wean 9. that they provide on Show the rate of Change Something were to Imove from point (2,1) the xy-Coordinate system be in the direction of de vedor (3,2).