Q.4 (a) Calculate the Gradient, . F (x, y, z) =- x+ y+ z ·j+ x+ y + z x+ y+ z

Q: Find the gradient of the function z = cos(x2 + y2), at the given point (3, −4)

A: Given=z=cos x2+y2 at point x,y=3,-4Gradient∇x,y=fxx,yi+fyx,yjwhere fx,y=z=cos x2+y2

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 3y2 + 5, (1, 5) Vf(1, 5) =

A:

Q: 7. Given the function f(x, y, z) = x² + y² + z² + xy + xz, find the gradient at P(1,2,1).

A: Must Know : Gradient function is given by ∇f=∂f∂xi+∂f∂yj+∂f∂zkGiven : f(x,y,z)=x2+y2+z2+xy+xz…

Q: ,2 For function f (x, y) x2+1 Evaluate the gradient at the point (1,2)

A:

Q: 5. If the gradient of f(r, y) at (1,2) is 2i – 2j, then the maximum and minimum values for a…

A: As per honor code, we are entitled to solve only 1 question at a time so I am providing you the…

Q: f(x,y)=x² +16xy + y² +8

A:

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 4, (1, 2) Vf(1, 2) =

A:

Q: A. Find the gradient of the function. f(x,y. z) = 3x y + cos(32)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the gradient of the function f(x,y,z) = x2 + y3 - 2z + z In x at point P (2, 2,1) %3D

A:

Q: Find the gradient of the function at the given point. In(x2 - y) - 2, (2, 3) Z = Vz(2, 3) =

A:

Q: Find the gradient of the function at the given point. In(x2 - y) - 6, (2, 3) Z = Vz(2, 3) = %3!

A: To find out the gradient of the function at the given point..

Q: Find the gradient of the function at the given point. w = x tan(y + z), (10, 5, –3) Vw(10, 5, –3) =

A:

Q: Let f(x, y) = exy and P(1, 0). Solve for the gradient of f at the point P.

A:

Q: Which of the following is the gradient vector of the function f(x, y) = 3x ln 3y - 2x²y at point (1,…

A:

Q: Find the gradient of the function at the given point. g(x, y) = 11xe/x, (4,0) Vg(4, 0) =

A:

Q: Find the gradient of the function at the given point g(x, y) = 2xe/x, (16, 0) Vg(16, 0) =

A:

Q: The gradient of f(x,y,z)=xy2z3f(x,y,z)=xy2z3 at the point (1, 1, 1) is

A:

Q: Find the gradient of the function at the given point. w = x tan(y + z), (9, 8, –3) Vw(9, 8, -3) =

A:

Q: 1. Determine if the gradient of the following velocity function is irrotational: V (x, y, z) = 3x³y²…

A:

Q: Find the gradient of the function at the given point. In(x² – y) - 9, (3, 8) z = Vz(3, 8) =

A:

Q: 5) Find the gradient of o = x?yz + 4xz2 at (1, -2, -1).

A:

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 3y2 + 2, (3, 5) Vf(3, 5) =

A: Given: fx,y=2x+3y2+2 ; Px,y=3,5   As we know that; The expression for the gradient vector.…

Q: 1. Find the Gradient of the following F = x*e" - y': b. F, = 4x - 3y + 5=? а.

A:

Q: The function f whose gradient vector is vf(x,y) = (xIn(v + 7), 7x + y + 7> has two critical points…

A:

Q: Consider the function g(x,y) = Y In(xy) + 2 and the point P(-1, -. Determine the following: (a) the…

A:

Q: Compute the gradient Vf of the function f given by f(x, y) + y at an arbitrary point (x, y). Then…

A:

Q: Find the gradient of the function at the given poin In(x² - y) -2, (3,8) X Vz(3, 8) = Z =

A: We are asked to find the gradient of the function.

Q: Find the gradient of the function at the given point. w = x tan(y + z), (17, 6, -3)

A:

Q: Find the gradient of the function f(x, y) = 3x + 5y2 + 1, at the given point      (2, 1)

A: Given equation - f(x,y) = 3x+5y2+1We can write it as - y = 3x+5y2+1Gradient is given by , dydxNow…

Q: Find the gradient of f(x,y,z) = (x² + y² +z²) ¯ - 1/2 Vf(-21.-2)=(1+Dj+k (Type integers or…

A: topic - gradient of a function

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: 1. Find the Gradient of the following a. F, = x'e" - y': b. F, = 4x' - 3y +5=?

A: Solution is given as below:

Q: Find the gradient of the function at the given point. In(x2 – y) – 9, (3, 8) z = Vz(3, 8) =

A: use partial derivative for finding the gradient.

Q: Find the gradient of the function at the given point. w = x tan(y + z), (19, 5, -1)

A: To find the gradient of the function at the given point.

Q: Find the gradient of the function at the given point. w = x tan(y + z), (19, 7, -4) Vw(19, 7, –4) =

A:

Q: Find the gradient of the function at the given point. In(x - y)- 4, (3, 8) Z = Vz(3, 8) =

A: The objective is to find the gradient function at the given point.

Q: -1/2 Find the gradient of f(xy.z) = (x² +y² +z?) + In (xyz) at the point (2, – 1, - 2).

A: To find the gradient of a…

Q: By utilizing Gradient Descent where initial x1=x2=Dx3%3D0, What is the approximated min. point of…

A: To find - By utilizing Gradient Descent where initial x1 = x2 = x3 = 0, What is the approximated…

Q: 6. Find the gradient of f(x,y) = ,x' - u°. grad f i +

A: We will find the first order partial derivatives with respect to x & y and use the definition of…

Q: Find the gradient of the function at the given point. In(x²-y)-3, (3,8) X Vz(3, 8) = Z

A: for finding gradient we have to find the derivative with respect to x and y   z  = ln(x2 -y)/x - 3…

Q: 1. Consider the function f (x, y, z) = 2°y – xyzešzy Compute the gradient of f.

A: Let's find.

Q: B. Find the gradient of the function at the given point. 1 f(x, y, z) = (x² + y² + z²)¯2 + In (x y…

A:

Q: Find the gradient of the function at the given point. In(x2 – y) - 3, (3, 8) Z = | Vz(3, 8) =

A:

Q: Find the gradient of the function at the given point. In(x² - y) - 9, (2, 3) = Z Vz(2, 3) =

A:

Q: Find the gradient of the function at the given point. w = x tan(y + z), (12, 7, -2) Vw(12, 7, -2) =

A: Gradient of function wx, y, z=xtany+z at point 12, 7, -2

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y² + 4, (1, 2) Vf(1, 2) =

A:

Q: Find the gradient of the function w = 6xy − y2 + 2xyz3, at the given point  (−1,  5, −1)

A: To find the gradient, take the derivative of the function with respect to x,y,z.