4. Prove that the vector given by (2xy -y')7+(2x²y-3xy² +2) 7 is a gradient. Also, find the function having the given vector as its gradient.

Q: Suppose you are climbing a hill whose shape is given by the equation z = 1000 −0.005x2 −0.01y2 where…

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

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

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Q: a. What is the gradient at the point (4,0,1)?

A: Consider the given function fx,y,z=x2+y2+2z2+3.  The gradient of a function is given by,…

Q: Let 3 = (X'X)-¹X'Y as shown in class. Let y = w'ß, where w is a column vector. Show that Var(y) =…

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Q: Suppose that f: R² R² is a function such that f (1,2)= the linear approximation. (Use syntax like…

A: We have to estimate f (1.1, 2.01) using the linear approximation.

Q: B A' A is the point (3, 1). Bis the point (a, 11). The gradient of AB is 5/½ 7 4

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Q: 4 2 IF Ø = 2x2² - xy₁ FIND 01111 AT THE POINT (2-2,1)

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Q: 3-find the gradient of the function v if_w=(xy)/z at the point(1,-2,1), find the directional…

A: The answer provided below has been developed in a clear step by step manner.

Q: Sub Yに3yこ1 passes through the point (3, 1), where its gradient is ax +b 3 Ify = 1-2x find the value…

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Q: Find the linearization of z = f(x,y) at P(-3, 2) when f(-3, 2) = 2 and f-(-3, 2) = 1, fy(-3, 2) =…

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Q: For z = e"v In(ry): - Find the gradient of z when r= and y = 2 - Find the directional derivative of…

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Q: (1)-(9-1²₁.sin(√²²-9)). Find the domain of the vector function, r(t):

A: To find the domain of the given vector function

Q: Find the gradient of cos(xy) – 3y4 + 3 at the point (1,4) -

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Q: x^2y''-2xy'+2y=0; y1=x, y2=x^2 Verify that y1 and y2 are linearly independent

A: x^2y''-2xy'+2y=0; y1=x, y2=x^2 Verify that y1 and y2 are linearly independent

Q: Find a vector that gives the direction of maximum rate of increase for the 6xyz at (-1,2,1) (a)6(2i…

A: To find A vector that gives the direction of maximum rate of increase.

Q: Choose the gradient of f(x, y) = x²y³. (a) 2xi +3y²j, (b) (c) 2xy³i+3x²y²j, (d) x²i+y³j, y³i+x²j.

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