If f (z) = zis a real valued function of a complex variable, which of the following can be the domain of f %3D OD= {x+iy|æ, y E R} D={x+iy|x, y € R, x = 0, Y= 0} |D={x+iy|x,Y E R, x = 0 OR y = 0} OD= {x+iy|x, y E R, y = 2x}

Q: Show that the equation Fu 1 u 0x² ² 3t² 0 is satisfied by u=f(x+ct) + F(x-ct) where fand F are…

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Q: .3 If U = 2– x, | x 2-xdx=

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Q: Solve for the orthogonal traysctories x*(3k-x) - ky². = x ? 2

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Q: Find if x'y+y' = x dy dx A) 2x+2y 1-2xy-2y B) x2 1-2ху C) x2+2y D) O A O B O c O D

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Q: (x, y, z) = 2x²y — xz² + 3y²z. Xyx

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Q: Suppose that f(z, y) = 10z²y² + 8z? + 2y? then find the discriminant of f.

A: We have to find the discriminant of the function of two variables fx, y. It is given that the…

Q: +タ x2 – 1

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Q: Find mZX (3y-71° X Y (2x) O W (x+181° (3y + 1)º

A: Solve for the angle X

Q: Integrate the function. 16x +즐 + C V16 -2 8 sin 1 +C 2 V16-2 +C + 16V16 - x2 8x - W16-2 +C

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Q: F(x, y) := x² + xy + y² – 1 y – x2

A: Solve the given problem.

Q: Determine if F = x²yî + (xyz +29)ĵ – x²y²k is conservative or not %3D

A: For vector field F⇀=ui^+vj^+wk^ Curl(F)=i^j^k^∂∂x∂∂y∂∂zuvw   For vector field F⇀ to be conservative…

Q: Consider the difference equation = Xn+1 Xn+bsin(2xn). Determine any fixed points of this difference…

A: Given difference equation isxn+1​=xn​+bsin(2πxn​) -----------------(I)Step 1: First, we find the…

Q: a z = 4x³-6x²y²-y com x= 2sen(t) y=-3cos(t) e

A: #As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Let f(x,y) = 8x - 2y + 5. Find the following values of f(x,y) for the given coordinates. (a) f(2,…

A: Given  f(x,y)=8x-2y+5 Find:f(2,-1) Substituting x=2 and y=-1 in the given equation, we get  f(2,…

Q: = Evaluate S₁2₁,22,23] f (2) dz where 21 = −i, z2 = 2 + 5i, zg 5i and f(x + y) = x² + iy

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Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

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Q: Find fy (-1,-4,-2) if f(x, y, z) = x³ z4 + 2xy – y? z + 1.

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Q: Zez analytical function or not?

A: We check whether w=zez is analytic function or not.

Q: What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy…

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Q: if r'y-- 2y + 1.

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Q: find the derivative of (2³ + j)² O 23 +j O 223 + j O 625 + j6z² O 325 + j3z?

A: Derivative of (z3+j)2 is 2(z3+j)2-1(3z2+0) = 2(z3+j)×3z2 = 6z2(z3+j) = 6z5+j6z2

Q: Find // VdA, + 1 R -dA, R= [0,3] × [−1,1]

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Q: the doi n ain of the functions

A: We have given two functions : f(x,y)=1xy…

Q: Determine which of the following pairs of functions are linearly independent. NO_ANSWER 1. f(0) =…

A: The linear dependency of functions can be evaluated using the value of the Wronskian of those…

Q: For the given function 6=x²yz C=3x²yi+yz²j-xzk and Find 82 Sysz (c) at point (1, -2, -1).

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Q: If f.(x, y) = 13x + 8y + 11, || f.(3, 2) = a. b. f„(5, 2)

A: Given, fx(x,y) = 13x + 8y + 11 a). fx(3,2) = 13*3 + 8*2 + 11 = 39+16+11 => fx(3,2) = 66

Q: Consider the function y -62 Which of the following statements is true for y? = ze Oy" = 36y…

A: Given,

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: