GRAD, DIV, CURL, V², DIRECTIONAL DERIVATIVE 36-45 Let f zy + yx, v = = Find 36. grad f and ƒ grad ƒ at (3, 4, 0) [y, z, 4z − x], w = [y², z², x²].

Q: Let = (3, 4, 12) . Find the directional derivative of f(z, y, 2) =1– y² +32³ in the direction of v.

A: Consider the given function, fx,y,z=x-y2+3z3 and v=3,4,12 Now, find the derivative of the function…

Q: L(cos3t) = S .a O s²+9 S .b O s+9 s2 –9 3 s2+9

A:

Q: Let M (2,1,3) and N(5,5,15) be two points. Find the derivative of the function f (x, y, z) = xy + yz…

A:

Q: 37. (grad ƒ) × grad f, (grad f) grad f

A: Follow the steps for question 37).

Q: Find the derivative of the function at the given point in the direction of A. f(x, y) = -10x2 + 5y,…

A: This question is related to directional derivative of a function, we will solve it by finding…

Q: Let a(t)-(1+t,t?,2+t?), then the equation of the tangent line at t-1 is: (2+t,-1+2t,3+2t)…

A: Here, a'(t)=(1,2t,2t)a'(1)=(1,2,2)anda(1)=(2,1,3)

Q: 21. Reflect in the y-axis. 5- 4- 2+ х -2 -3+ -4 T'(2, 2), V'(4, 1), W'(5, 4), X'(0, 4) b. T(-2, -2),…

A:

Q: Considering the following graph of the given function f. y The xy-coordinate plane is given. The…

A:

Q: 9. (Chapter 10, #20) Prove that for every n E N, (1+2+3+ · ..+n)2 = 13 + 23 + 33 + ...+ n³.

A: To prove the result ''∀n∈N,1+2+3+...+n2=13+23+33+...+n3'' by Mathematical induction: First prove for…

Q: determine line of reflection

A: We can determine the line of reflection in the below steps.

Q: Pls help ASAP. Pls show all work.

A: Given, y=14 Aim : Find derivative

Q: The temperature on a cubic box [0, 4] × [0, 4] × [0, 4] (measured in meters) can be described by the…

A: Function, Tx, y, z=x2y+y2z

Q: (4) Calculate faz, fyy, and fry when f(x, y) = 2x4y³.

A:

Q: of find 4x + 9y of and dy For the function f(x,y) = %3D of dx ||

A: We can answer this question as below

Q: nd the directional derivative of f at P in the direction of a. f(x, y, z) = xy + z²; P(-1,-1,-3);…

A: We have used definition of the directional derivative.

Q: T/f Two parallel lines in the 2d plane never intersect each other

A: Given that two parallel lines in the 2D plane never intersect each other. Here we have to determine…

Q: derivative of f(x, y, z) = x + z at P(6,5,-5) in the direction from P to Q(5,7, -4). NOTE: Enter the…

A: We can solve this as follows:

Q: = Evaluate and at the point (7, 7, «) using the implicit relation sin(z + y) + sin(y + z) + sin(z +…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: A set of direction numbers for the tangent line to the curve of intersection of S : x² + y² – z = 8…

A: The equation of a tangent line to a given surface involves the gradient of the function. When we…

Q: Find the directional derivative of f(x, y, z) = xy + z³ at the point P = (3,-4, -3) in the direction…

A: