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- Calculate directional derivatives and gradients in three dimensions. Find an equation for the tangent plane to the surface z + 4 = xy° cos(2) at the point (4, 1, 0).Use the gradient vector to find the equation of the tangent plane to the surface x? + y? - at the point (2,2,4). Write your answer in the form Ax + By + Cz = D.4. A wheel is rotating about the line y = x, z = 0 with angular speed w = 10 sec-. Find the velocity and speed of a body at the point (4, 2,-2). | 5. v = y, -x is the velocity field of a body moving along a path. Find the corresponding equation of the path in the cartesian coordinates and assign v to various points of the path.
- 1.) Let s(t)= tlnt-t be the displacement of a particle (in feet) from the origin after t seconds. a.) Find the velocity of the particle at 5 seconds. (Show all your work and include units) b.) Find the acceleration of the particle after 5 seconds. (Show all your work and include units)Find the directional derivative of ø = x² + y² + z² at point (1, 2, 1) for a direction determined by dx = 2dy = -2dz.A sky diver weighing 192 lb (including equipment) falls vertically downward from a very high altitude. Assume that the air resistance is proportional to the falling velocity with the constant k = 0.6, the acceleration due to gravity g = 32ft/sec2, and that the positive direction is downward. What is the terminal velocity of the sky diver if he/she never opens the parachute?
- Find Components of the Acceleration For the curve defined by 7(t) = (e-t cos(t), eʻ sin(t)) find the unit tangent vector, unit normal vector, normal acceleration, and tangential acceleration at t = 3 T(플) - N(플) - 3 3 AN =Let f(x, y) = x²y + y²x. Find the directional derivative at (-3, 2) in the direction = π/2. Duf(-3,2) =