Consider the vector field Find a direction (8) sin (a) in which the directional derivative of f(z,y), at the point (z,y) = (0,5), has a value of 1. f CHULE TENEN BOO 8 00 P f(z,y) = 19 zv C
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- Find the directional derivative of g(a, b) = cos(3a + 4b) at the π point ( along the direction of the vector (-4,-3)Find the directional derivative of the scalar field = x³y + 4xz at the point (1,-1, 2) along the direction vector (2, -1, −2):Find the directional derivative of the scalar field þ= x¹y + 4xz at the point (2, -2, 4) along the direction vector (2, -1, -2):
- 4. Determine the directional derivatives of +V3 sin" xy $(x, y) =tan at the point (1,1) in the direction of the vector 31-2j .Compute the directional derivative of the function f(x,y) = 5xy – 5y at the point P(-5, - 3) in the direction of the vector (- 2,2). The directional derivative is (Type an exact answer using radicals as needed.)A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)
- An airplane took off from point (3, 0, 0) at an initial velocity, v(0)= 3j with an acceleration vector of a(t) = (-3 cos t)i + (-3 sin t)j + 2k. Determine the vector function, r(t), to represent the path of the airplane as a function of t.Compute the directional derivative off at the given point in the direction of the indicated vector. f(x, y) = ³x²-y, (1, 3), u in the direction of -2i-j Du f(1, 3) =Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the unit vector u = cos @i + sin @j. f(x, y) = Р(3, 0), e = -. 8x + y
- Compute the directional derivative of g(x,y)=sin(pi(5x-5y)) at point P(1,-3) in the direction (15/17, 8/17). Be sure to use a unit vector for the direction vector.Consider the function f (x, y) = 5x² - 6y². Find the directional derivative of f at the point (−1, −4) in the direction given by the angle = (Here is the polar angle -- the angle which the direction makes with the positive direction of the x-axis.) Find the unit vector in the direction in which f is increasing most rapidly at (-1,-4).Compute the directional derivative of the following function at the given point P in the direction of the given vector. f(r, y) = In(5r+4y) on P(3,9), ū= 6i+8}