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…

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Q: Q4: Find the derivative of the function at P, in the direction of A 2 1) f(x, y) = 2xy-3y², P.…

A: According to our guidelines we can answer only one question and rest can be reposted.

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.

Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1,1) in the direction of from the…

A: We have to find the directional derivative.

Q: The directional derivative of f(z, V, z) =y-vz at the point (2, 1,1), in the direction of the…

A: We have to find directional derivative of given function f in the direction of tangent line of the…

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…

Q: The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2x + y = 3 is given by…

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Q: The equation of the line tangent to the curve F (x) = S e dt at a = %3D V1- O y-V2 = (=- ) O %3D y -…

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Q: Find the derivative of f(z) = In(z -+ O (A) f'(2) = 2² – 3z + 2i). | --2 V:-3:+2; 1 AB) ƒ'(2) = V-3:…

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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: F(x,y) = In x+y of the function at the point %3D P( 3,4) ond V= [ = -7+ 2 find the derivative %3D in…

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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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