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3. Find the maximum rate of change of f(x, y) = e-ry at (1, 1) and...
(1 point) Find the maximum rate of change of f(x,y) = ln(x2 + y²) at the point (-2,-5) and the direction in which it occurs. Maximum rate of change: Direction (unit vector) in which it occurs:
Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 5 sin(xy), (0,8) maximum rate of change direction vector
Find the square of the maximum rate of change of f (, y) = xy + 2 (x) at the point (4,6), wherer (2) =42. The square of the maximum rate of change of the function is
2.10.4 Given a function f(x,y) on a compact region E in R^2, Find the maximum and minimum values of f on E, and the points at which these extreme values are attained. f(x, y) = x2 sin y + x, and E is the filled rectangle where -1 < x < 1 and | 0 < a < .
s (ls points) 1/ Given f(x,>)-xy+e" sin y and P(1,0) a) Find the directional derivative of fat P in the direction of Q(2, 5). b) Find the directions in which the function increases and decreases most rapidly atP e) Find the maximum value of the directional derivative of fat P. d) Is there a direction u in which the directional derivative o f fat P equals 1? If there is, find u. If there is no such direction, explain. e)...
please circle the answer! (1 point) Suppose f (x, y) = , P = (1, 3) and v 3i - 2j A. Find the gradient of f Vf = i+ j Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (Vf) (P) it j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Duf...
6 (15%). Find the rate of change of f(x, y, z) = x/(y + 22) when we move away from the point (4, 2, 1) in the direction (3, 4).
2 + COS- 2.ry dy d 1+y2 = y(y + sin x), 7(0) = 1. 3. [2cy cos(x+y) - sin x) dx + x2 cos (+²y) dy = 0. 4. Determine the values of the constants r and s such that (x,y) = x'y is an Integrating Factor for the following DE. (2y + 4x^y)dr + (4.6y +32)dy = 0. 2. C = -1 You need to find the solution in implicit form. 3. y = arcsin (C-cos) 4. r=...
1. Consider lim (z,y)=(0,0) 2 + y2 Compute the limit along the two lines y = 0 and yma. 2. Let F(x,y) = sin(x”y), where = sin(u) + cos(u) and y = ew. Use the chain rule (substitution will earn zero credit) to find 3. Find the maximum rate of change of f(x,y) - eat (1,1) and the direction in which it occurs.
Find the absolute maximum and minimum values of f(x, y) = x² + 4y? – 164 – 4 on D: the set of points (x, y) that satisfy x2 + y2 < 25. Part 1: Critical Points The critical points of f are: (0,2) M Part 2: Boundary Work Along the boundary f can be expressed by the one variable function: f = f(y) = (49-y^2)+9y^2-36y-3 Σ List all the points on this side of the boundary which could potentially...