41. (а) Let f(х, у) 2 + y2. Estimate fr(2,1) and fy(2, 1) using the contour...
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16, Figure 8.59 is a contour diagram for z f(x, y). Is positive or negative? Is fy positive or negative? Estimate f(2, 1), fz (2, 1), and fs(2, 1). -6 10 14 18 Figure 8.59
16, Figure 8.59 is a contour diagram for z f(x, y). Is positive or negative? Is fy positive or negative? Estimate f(2, 1), fz (2, 1), and fs(2, 1). -6 10 14 18 Figure 8.59
2.1(9pts) Consider thc following contour plot for thc arbitrary function f(x,y): Y 0 2 Х -1 + 1. What is vf(0,0). Why? 2. At the point (0,2), in what direction should one move to increase the fastest? 3. Which vector has the greater magnitude: Vf(-1,0) or f(2,0)? CS Scanned with CamScanner
Calculus III
1) Identify each of the following surfaces: а) z' %3x? - 5у" b) z 4x2-4 y c) z2+3x2-5y = 4 d) z2x23-5y e) у3х* 2) Find and classify all of the critical points for f(x, y)=xy -x2 + y'. 3) Find the maximum and minimum values of f(x,y)=xy over the ellipse х* + 2y %3D1. 4) Let fx, y) x3 -cosy a) Find the first order Taylor polynomial for f(x,y) based at (1,7). b) Find the sccond order...
1. (Section 5.1) Let f(x) . In this problem, we'll numerically estimate the area under the graph of f on [-2, 1] three different ways. (a) First, graph f on [-2,1] in Mathematica, and draw three neat copies of it on your paper for parts (b), (c), and (d). (b) Compute Rs. Show your work by drawing the rectangles you use on the graph of f. Based on your graph, is this a clear overestimate, a clear underestimate, or is...