Question 2 ( (a)(s) Compute the gradient of f. s) Consider the function f(x,y) (b) (F I T-Y e) Calculate the directional derivative D(-1,2) f(4,1). (c)(..) The level curve f(x, y) = 2 is in fact a line. Determine this line, and verify that it is orthogonal to the gradient at P(2, 1).

Q: Estimate the area under the line y= 2x+1 using six rectangles and right endponits over the interval…

A:

Q: Point is (lっ) Fix, ノ) = 3x what is the gradient?

A:

Q: Determine the directional derivative of f(x, y, z) = tan-1 221) where U = (-1,2,2) at P(0, 1, 1).…

A: The given function is fx,y,z=tan-1xy22z2-1. The direction vector is u=-1,2,2 and the point is…

Q: Find the gradient Vf and the directional derivative at the point P (1,–1,2) in the direction a =…

A: The given function f(x, y, z) = x3z - yx2 + z2.The gradient of a function f is defined as∇f(x, y, z)…

Q: If f(x, y, z) = 4zy², then the gradient at the point (5, 2,5) is Vf(5, 2, 5) =

A: Given that, f(x, y, z)=4zy2 Aim: Find ∇f5, 2, 5

Q: b. Find the angles 0 (with respect to the positive x-axis) associated with the directions of maximum…

A:

Q: 4) Let f(x, y) = x² – 2xy a) Find the gradient of f at the point (1, –2). b) Use the result of (a)…

A:

Q: Find the gradient of the function f(x, y, z) = z²e²y² When is the directional derivative of f a…

A: Given function: fx,y,z=z2exy2 To find: The gradient of the function. To conclude: a) when the…

Q: (10) Given: f (x, y, z) = %3D 2y-z a) Find the gradient of f (x, y, z). b) Find the derivative of f…

A: (a) Given function is fx, y, z=x2y-z.  The gradient of a function is defined as follows: ∇fx, y,…