[* [V²*³ ƒ(z,y) dz dy = "ƒ(x, LS 3. Change the order of integration. y) dr dy = '"* ftal") ƒ(x, y) dy de, find $1(2) and 42(2). 0 $1(x)

Q: The power series solution for the differential equation (4-x²)y" + 2y = 0 can be generated from the…

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Q: Find the derivative of the function h (x, y, z) = cos xy+ e+ In zx %3D at P. (1, 0, 1/2), in the…

A: Here we have to find directional derivative of h(x,y,z) in the direction of u.

Q: dy using implicit differentiation: 4x°y² – /æ +3y = 57 Find dx %3D O dy -20z'y² + }a¯1/2 8r°y+ 3 dz

A: Given,            4x5y2 -x + 3y =57

Q: B. Water is flowing out of tank at a rate of 200 – period. How much water flows out of the tank in…

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Q: (10) Find x²e*y dx dy. (Hint: Reverse order of integration.)

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Q: The order and degree of the differential d³y V dy equation: 7+ i. - dx3 dx 3, 2 7,3, 3, 1 3, 7

A: The order of a differential equation is the highest order of the derivative that is present in that…

Q: dx + 3tx = t4 Int+1, dt 2. t2. %3D

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Q: Q2: Evaluate the following: (answer only two) (a ) S2 dy f, sinx dx (b ) S, dx f* dy S**-y dz +y-1

A: Integration

Q: Im kind of confused with the integration of (y-1), can it also be ((y2)/2)-y?

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Q: Find the derivative of the function at Po in the direction of A. 1(x.y.z) = - 2 e* cos (yz),…

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Q: A cylindrical vessel without lid is 4 cm in radius and 10 cm in height. If the vessel is to be…

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Q: w =sec (xyz) - Yx +y+z

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Q: Calculate the gradient of the following function fox, y) = (x – 2)^3 sin y, at (0,0]

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Q: Find the total differential of the function f(x, y, z) = 4 ryz2 df ? dx + ? dy + ? dz

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Q: Find of / dx and of / dy. f(x,y) = e(x+ y + 9) of / dx = df / dy =

A: Let f be a function of x and y. The expression ∂f∂x implies that partial derivative of f with…

Q: complementry function for this DE  12.7y" + 68.58y' + 153y = 0.289(y+1)

A: Given is a differential equation:12.7y''+68.58y'+153y=0.289y+1To find the complementary equation of…

Q: Determine the required integrating factor: y'=x-2y cot (2x) O sec (2x) O2cos (2x) O2cot (2x) O sin…

A: y' =x-2ycot2x

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = − 6 e* cos (yz),…

A: The given function is  and the direction  at .The aim is to find the derivative .

Q: a) = 2, giving your answer to 2 decimal places if Find the gradient of the curve y at the point a…

A: Given function  Gradient of function y is given as follows

Q: Let z be a differentiable function of x and y related by the following equation: x+z (√y + cosh(z))…

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Q: 3). Consider the system 2 ()' - (²₂3) (1). = -2 - (a) Plot the solution curve passing through the…

A: Matrix differentiation is done row or column wise.

Q: Find the derivative of the function at Po in the direction of A f(x,y,z) = 3 e* cos (yz), Po(0,0,0),…

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Q: of of For the function f(x,y) = 4x* - 3y' - 8, find and dx of %3D dx of

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Q: 1. Use the differential df to approximate the change in the value of f(x,y) from the point (1,0) to…

A: We will be using definition.

Q: Find the derivative of the function at P.(0,0,0) in the direction of B. f(x, y, z) = 3e* cos yz,…

A: Directional derivative of the function.

Q: dy Using the parametric differentiation find dx if x = 10e10t, = 4e20t Y 5.00 e10t O 1.20 e10t 0.80…

A: x= 10e10t  y = 4e20t