If u(x, y) = -e2* sin(2y – 1) and f(x) = u(x, y) + iv(x, y) is analytic, then f(z) = %3D O je2z-i O None of them e2z+i ie2z+i

Q: Find the constants a and b such that the complex function f(z) = x² + ay² - 2xy + bx²i − y²i + 2xyi,…

A: A function f(z)=u+iv is analytic if ∂u∂x =∂v∂y and ∂u∂y =-∂v∂xGiven…

Q: For the linear operator L = D^2 −4D + 8, determine L(y) for y = e^(2t), y = e^(2t)sin(2t), and y =…

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Q: If cos(4x – y) = x+y, then dx A -1 - sin(4x – y) 2+4 sin(4x-y) (B) sin(4x-y) 1 1+sin(4x-y) C) 1+4…

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Q: Find nd cos(z ² + y²)dA where D = {(x, y) | 16 ≤ x² + y² ≤ 81} D

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Q: For the relation siny – y² =x²y– x+x , is dx 3x²y+1 А. cos y – 2y –x T – 1 3x² + 2y – cos y cos y –…

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Q: The function u(x, y) obeys, 8²u Ərəy = -2e

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Q: Let f(x, y) = + tan(xy – x³) , find дудх x-4y5 O a. 80y4 + sec2(xy – x³)(1+ (xy – 3x³) tan(xy – x³))…

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Q: 4x = 0 %3D 4y + i = 0 x + y 8 = 0 (х, у, 1) %3

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Q: Use the gradient to find the directional derivative of the function at P in the direction of Q f(x,…

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Q: If f(x.y,z)= y + xz then f ,(1,1,1) =

A: The given function is  f(x, y, z) = y5 + xz

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.