Q1] Find the derivative of f(x, y) = x2e-2y at po (1,2) in the direction of v =i+j. In what directions does f change most rapidly at p, and what are the rates of change in these directions? %3D Q2] (Choose only one) a) Use the Chain rule to find the derivative of z e*y with respect tot along the path x t cost and y =t sin t. What is the derivative's value at t n/2 az and ax az b) Find given that xy + z + sin(xyz) = 0. ay Q3] For the following integrals, write an equivalent double integral with the order of integration reversed. r1 (3-2x a) So S f(x,y) dydx (8 Marks) b) S S, F(x, y) dxdy (7 Marks) Q4] Use double integrals to find the area of the region that lies inside the cardioid r = 1+ cos 0 and outside the circle r =1.

Q: z + 2.5 -3 = Z

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Q: Find the directions in which f increases and decreases most rapidly at point P. Then find the…

A: As per guidelines, we will solve first question only.

Q: Q4: Find the derivative of the function at P. in the direction of A 2) g(x, y) = x - (y² /x)+ J3…

A:

Q: Find directional derivative for f(x,y) = y +, Xo = 4, yo = 5, nx = 1, ny = 0. df ðf af -Nx + -Ny=|…

A: We will evaluate the required values.

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A: We have to find the directional derivative.

Q: Answer all questions

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A:

Q: 1 log3(r – y)*

A: Given; fx,y=1log3x-y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

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A:

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Q: 04:- Use the Chain rule to find the derivative ) of z = 3x2 - 2 xy y and If x=x (u, v) = 3u + 2v and…

A: Please refer to the image below.

Q: Find the directions in which f increases and decreases most rapidly at point P. Then find the…

A: Step:-1

Q: Find an equation for the slope of the graph of y= 2x + 5x2 -2x at any point. Am= 6x2 Bm= 6x2 + 10x…

A: Given y=2x3+5x2-2x

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Q: Find the derivative of using the chain rule: f(x)= csc x^3 answer the question correctly and…

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Q: (d) Compute the driectional derivative of f at (1,2) in the direc- tion u = (e) • point (1, 2)? What…

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