Q2: Discuss the fundamental theorem for gradients using E = 5x2 i + 20 xy j+ 10 yz3 k and the following paths: %3D (a) (0,0,0) (1,0, 0)(1, 1, 0) (1. 1, 1); (b) (0,0,0)(0, 0, 1) (0, 1. I)(1.1, 1):

Q: Fincl the gradient (m)a Joining of the tne the Points (2,8) and (3,2)

A: Gradient: The tangent of the angle that a straight line makes with the positive direction of x-axis,…

Q: Q1. Decide which of the following functions are linear transformation? T hope for a clear solution…

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Q: What is the gradient of the function f(x) = 2 e3x + 5 e7× 2 e3x 6 er +5 ex 5 e* F 2 ed + 35 e* 2+5…

A: The gradient function gives the slope of a function at any single point on its curve.

Q: b Suppose we want to find all points at which the direction of fastest change of the function f(x,…

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Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y² +6, (3, 1) Vf(3, 1) =

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Q: (c) Vf(x, y, z) = (2xy, x² – 2yz, 4 - y²) -

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Q: We want to estimate f(1.01 , 0.97) for the function f(x,y)= √(4 - x2 - y2). For this, we can use an…

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Q: f(x) = x2 + x and so f(1) = 1 + 1 = 2 We want to approximate the slope at x = 1 using the slope…

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Q: IT i=1 3 - 레페루 = (2) |T|| U

A: The conjugate gradient method is a mathematical technique that can be useful for the optimization of…

Q: Let f(x, y) = x² – y?. Find (c) The linearization of f at the point (2, –3).

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Q: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

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Q: 2. Find the values of k if the points (0,0), (2, 3k) and (4k, 6) are collinear. 3. The line joining…

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

Q: 15. Consider the curve y 9 X + 1 x-1 Find the x-coordinates of the points on the curve where the…

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Q: Question 2. Consider the function f(x, y) = x³-12xy + 8y³. (a) Find all the stationary points of the…

A: The saddle point is (0, 0)  Local minima is (2, 1)

Q: 4. xyzx + 2y³ (2)³ = 1 Dependent variable/s: Independent variable/s: Type: Order: Degree: Linearity:

A: Solution :  To discuss about the nature of given differential equations

Q: For what values of x will the curve of y = x(x² – 12) has zero gradient? %3D

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Q: (b) By determining constants c,, C2, C3 and c4, which are not all zero and are such that cifi(x) +…

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Q: (c) f(x1,x2, x3, X4) = 4x1 + 5x2 – X3 + x4 - (d) f(x1,x2, X3, X4) = -5 exp(x1)+ x2 · X4

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Q: PROBLEMS ON THE GRADIENT If 6(x, y, z) = 2x z-x'y, find Vo and Vol at the point (2,-2,-1). PROBLEM…

A: Given: ϕx, y, z=2xz4-x2y To find: ∇ϕ and ∇ϕ at the point 2, -2, -1.

Q: Question 3 a. Find the gradient of r=x +y² + z?

A: The given problem is to find the gradient of given function r=√(x2+y2+z2) , we have to find the…

Q: Q.8 Find the gradient Vw ofthe function w = In /x² + y² + z². %3D

A: Given function W=ln(√(x2+y2+z2)) Now we will find the gradient as shown below

Q: 1. Find the gradient of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1,-1). 2. Find the…

A: The given function is f(x,y,z)=ln(xy)-zx2 We have to find the Gradient of the f(x,y,z)=ln(xy)-zx2 at…