An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y). where i = -1. If u(x, y) = x2 - y?, then expression for v(x, y) in terms of x, y and a general constant c would be

Q: Find the derivative of the function. 10) y = (x + 1)2(x2 + 1)-3 2(x + 1)(2x2 + 3x - 1) (x2 + 1)4…

A: Given:        y= x+12x2+1-3

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Q: By Lagrange's formula, prove that y =y3-0-3(ys-y- 3) + 0-2 (y_ 3 -y_5).

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Q: 3) Show that the function 13-212+2 g(2) = is a Complex differontiable function ait the point 20 =1…

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Q: Find the derivative of the function. 8) q =V10r - 15 -5r4 A) - V10r -15 B) 2/10r - 15 C)- 2/10 - 514…

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Q: · Use the definition of the derivative of complex function to show that f(z) is not dif- ferentiable…

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Q: Part 1 a) Given f (z) = + x2 + i(2x2 - y?), show which points where f has y a derivative. b) Show…

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A: Linearization of a function g(t,u) about (a,b) is  L(t,u)=g(a,b)+(t-a)gt(a,b)+(u-b)gu(a,b)

Q: Differentiate: 3 a) F(y) = ( (y + 5y³) x²e* b) f (x) : x2+ex А c) f (x) : B+Cex

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Q: 3) a) Find the real and imaginary parts of the following functions: Z-1 ^) f(2)= 2² +₁ Z +4 f(z) =…

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Q: u = x² + y³ + z*, X = s•t = s2 +t2 y = z = s-t

A: We find complex function

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A: Given that the tangent plane to the function f(x,y)=ln⁡(ax2y+bxy+c) is z=−6x−y−3 at the point…

Q: In physical chemistry, it is shown that the pressure P of a gas is related to the volume and…

A: Given- In physical chemistry, it is shown that the Pressure P of a gas is related to the volume and…

Q: 13. In y = what is the derivative of 2x2 +3? x+1 a) 2x b) 4x c) 4x +3 d) 7

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Q: For f(r, v) = + find f(3,4) and state the domain of S(1, y).

A: We are given the two variable function here. To find the value f(3,4) we will simply put x=3 and…

Q: 5) The equations r² + y²s + yt² - 13 and y² + x²s + rt² = 9 define s and t as implicit Əs functions…

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Q: show that the function 3x²y-y³ ty is he harmonic and then find it's Harmonic conjugate v (x, y)

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Q: 2. In y = c+ C2*

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A: We use chain rule

Q: he equations æy² + 8xzcos(u) + ye" = 16 and x yz + xe" – 5u²v² = 15 are solved or u and v as…

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Q: For two points (x1, y1) and  (x2, y2) such that xi > 0, yi > 0 for i = 1, 2, we say  (x2,…

A: There are about 4 functions provided.To show:They are Schur convex or not.Concept used:i) Any…

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

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Q: 9) Find a linear function of the form f(x) = ax +b that satisfy the conditions A-4) = 8 and (3) - 9.

A: f(x) = ax+bf(-4) = 8→ -4a+b = 8.........................1f(3) = 9→3a +b =…

Q: |(0,3) C1:x2 + y? = 9. (-3,0) C2 (3,0) Figure 1 Based on Figure 1 and given that F = y²i + (3xy +…

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Q: 4y² Given the function f(x,y)= +e*y _find each of the following. SIMPLIFY

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Q: If B = x°ya, + (2x + y)a, – (y – 2)a, find (a) V B (b) V X B (c) V (V B) (d) V x V X B

A: Given : B=x2yax +(2x2+y)ay - (y-z)az

Q: Let z be a differentiable function of x and y related by the following equation: x + ² =(√y +…

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