e (²+1)5 sin f(z) = sin ³ z 2³(2-3i)² # Compute the residue Res(f; zo), where zo is the pole.

Q: + ax ax²y + bxy² + 2y³ be (x, y) its harmonic conj en la + b + v(1, 1) is ec

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Q: 1] Evaluate (a) -S (s²+1) ² {t sin (b) S 1/2 5² (s² +¹)² (d) S

A: Find Laplace of tsin(t/2)

Q: 3. Show that the complex function f(z)= cscz =1/ sinz satisfies the Cauchy-Riemann condition. Find…

A: The given function is fz=cscz=1sinz. A function fz=ux,y+ivx,y, satisfies Cauchy Riemann equations…

Q: O [-5, -1) U (1,6] O (-5,6] O [-5, 6] O (-5, -1] U [1, 6] Find the domain of r(t) = (ln(t + 5),…

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Q: The imaginary part of the complex function f (z) is, v(x, y) == x* –- 6x²y² + y* (i) Prove that v(x,…

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Q: sin(2t). Find Əz Ət if z = √r² + s², r = cos(2t) and s =

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Q: (D2 -4D +7)y = 0 A y = e²"(c,cos/2x+c,sin/2x) COS y = e2"(c,cos/3x+c,sin/3x) В © y = e (c…

A: 1. Given differential equation is (D2-4D+7)y = 0 Here Auxiliary equation is D2-4D+7 = 0⇒ D = 4 ± 16…

Q: a) 2(sin x)² - 1 = 0 [0,2π]

A: a) 2(sin⁡x)2−1=0[0,2π]

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Determine the…

A: We will use concept of arc length in 3d We want to determine the length of a vector function,…

Q: 5. Find L{f(t)} a. f(t) = sin?(t) + t b. f(t) = n² – 8e¬2t + (et + 1)² | c. f(t) = F, sin yt -cos…

A: As per our limit we can solve only first three subdivisions if you want the answer for other…

Q: c) Let f(x, y,z) = cos (xyz)sin(x²y=

A: The given function is f(x,y,z)=cos2(xyz)sin(x2y2z2) ..............(1) we have to find;  fx=∂f∂x=?and…

Q: Let r(t) = (sin (1), cos (1), 4 sin (r) + 5 cos (2r)). Find the projection of r (t) onto the…

A: We have been given:rt=sint, cost, 4sint+5cos2t. To Do:We have to find the projection of rt onto the…

Q: 8. Consider the function -2r y = c₁e² cos 2x + c₂e² sin 2x + c3 + C₁x + c5е¯¯² + c6e- +c7xe-2x with…

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Q: Find z where z = sin (æ²) cos (4²) COS

A: The given function is z=sinx2 cosy2.

Q: Show that fi (x) = x, f2(x) = cos 2x are orthogonal on

A: Given that, f1(x)= x, f2(x) =cos2x and interval is [0, 90o] Wehave to find that the functions are…

Q: Suppose f (x) =cos( 2– 3x). Evaluate: )dx A - 3sin(3x – 2) +C ® -;sin(3x – 2) + C sin(3x – 2) + C D…

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