3 Determine poles of the following function and residue at each pole z2 (z-1)(z-2)² 4 Evaluate sinz? dz (z-43 where C is zl=1

Q: 103. GU Plot the graph of f(x) sin mx sin nx on [0, 7] for the pairs (m, n) = (2, 4), (3, 5) and in…

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Q: TOTAL.40IMark uestion 5 a. Let f (x) = sin(ax + b) and let g (x) = cos(ax + b) where a and b are…

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Q: 2. Find the function that satisfies these conditions: 7 (t) = (e', sin t, sec² t); 7 (0) = (2, 2, 2)

A: Ffff

Q: sin TZ Let f (z) = Find the residue of f (z)at z = 3 (z – 3)2

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Q: Z-T 4. Find all singularities in C for the function f (z) = and their residues. sin? 7

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A: We have to find the residue of f(z)  at z=2

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A: Evaluate the Definite Integral : ∫π6π37cosxsinxdx

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A: Given, the function g(x)=sin2x,  if  0&lt;x≤π6ax+b,if π6&lt;x≤1. We have to find the value of a and…

Q: 27 Show that ø(x, y)= e*(x cos y –y sin y) is a harmonic function, and find the conjugate harmonic…

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Q: "(2) – 16f(2)) sinh(4x) dr Find the value of in terms of f(0) if f(a) = f'(a) = 0. %3D f(0) O f(0)…

A: See the calculation below  Fourth option is correct

Q: Л 5n Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x== 4 A 1.414…

A: Here we have to find the area bounded by the given trigonometric curves.

Q: Determine the order of the poles for the given function. cos(z) - cos(22) f(z) Z= Pole Order

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Q: Q3:A. Determine the following function U is harmonic or not X y U = 3 + cos sin os sin B.Verify that…

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Q: (a) (b) Find the residue of f(z) = sin at z = π. Find the residue of f(z) 2²-3z 2²+4 at z = 2i. =

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Q: 10. Find the period of the function: g (x) = 3 tan (6z + 42) %3D 6. 42 3, kl3

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Q: 35. Eliminate the parameter t in the followin x = 9+4tant y = 4+4sect 36. Eliminate the parameter t…

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Q: Find +he obmain ond rage of the hallowing functions 1 i) Cos(x-T) ii) x²+x-2 iii) Lan:

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Q: 3.4 Find the residue of f(z) = (1 – 2®) sin(1/z). %3D

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Q: sin TZ Let f (2) = . Find the residue of f (z) at (z – 10)² - Z = 10.

A: We have to find the residue of the complex function fz=sinπzz-102 at z=10. Since we don't have…

Q: 2r + 9(x)+ sin(rx). (2) Let f(x) = g where g is a differentiable function such that )-1-4 ) - d(1) =…

A: Given: f(x)=g(2x+12g(x)+sin(πx))g(14)=1−22=1−12g'(14)=2π2=π2g'(1)=3f'(14)=?

Q: Q2: Show that u = ln(x² + y2) is harmonic function and find the conjugate harmonic v = (x. y) and…

A: Given: u(x, y)=lnx2+y2 To show: u(x, y) is harmonic function and find its harmonic conjugate v(x, y)…

Q: 1. Consider the function Y= Sin(5x) on the 0<x< %3D interval a) Determine where the graph of the…

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Q: π 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x = - to x = 4 4 (A)…

A: See the details solution in below

Q: 1 (27 x sin nxdx 27 bE f(x)sin nxdx -sin nx -1. 1-2n cos 2nn COs nx %3D %3D The requirod f 2)

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Q: 6. Determine whether the following functions are harmonic. (a) u(x, y) = 2e* cos3y and v(x, y) = 2e"…

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Q: Z-T 4. Find all singularities in C for the function f (z) and their residues. sin? z

A: We can solve this question using definition of singularities and residues

Q: -1. For the function f(x,y,z) = sin '(xyz), find fx, fy, and f₂. fx (Type an exact answer, using…

A: Given query is to find indicated derivative.

Q: (x²+y2 ) prove ne du + y ax -2 sin2u ( Euler's Rule) 5. If u = cot-1 that x ду x+y

A: We use the Euler's rule of partial differential in homogeneous function to solve this problem.

Q: the function f (2) = z Cos z ̟has a zero of order 1 None

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Q: Find extrenhum of one of the following function 1. 2(a, y) = sin2(x- 0.5) + artg (y- 0.5) rE (-1,1],…

A: Let us find the Extremum of the given function in the next steps.

Q: [4] Let f(x) = -p³ Position to find p2, P3, and p4. cos x and po = -1, pi = 0. Use the Method of…

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Q: a3z a3z 5. For z = x?siny show that дудхду ay²əx

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: 19.18. Show that each of the following functions call each one u(x, y)- is harmonic, and find the…

A: All the questions has been solved below.

Q: Q.3 (a) Show that the function u =e-2xy sin (x² – y²) is harmonic. (b) Test the analyticity of the…

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Q: 3. (a) Determine whether the function y=1-cosx is even, odd or neither. (b)Find antiderivative of 3…

A: Consider the given function as y=1-cosx. Check the function is odd or even as follows. let…

Q: sin TZ Let f (z) Find the residue of f (z) (z – 3)² at z = 3

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Q: Q1/ Evaluate the following [Choose six only). (1): 2 dx dy if y = 5 cos 2u and u = x + . (2): lim,…

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Q: 201 Q1: Locate the zeroes of the following functions and determine their order. 2) z³ sin(z - 1). 1)…

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Q: sin TZ Find the residue of f (z)at z= 6 (z – 6)² Let f (z)

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Q: 116. a. Show that if ƒ is odd on [-a, a], then f(x) dx = 0. -a b. Test the result in part (a) with…

A: a.  Now put

Q: Q2) A: If u = sin-()+ tan-(), prove that du ди x=+y дх ду = 0 ax ay n lim (1+ (1 + iV3)10 B: Find:…

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Q: π 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x=—. 4 4 (A)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 8. Find the value c that satisfies Rolle's Theorem for f(x) = cos x on 2 2 А. п/4 B. π 2 С. Зп/4 D.…

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Q: sin TZ Let f (z) = Find the (z – 10)² residue of f (2)at z = 10. -

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Q: 6 The coefficient of sin( 2x) in the antiderivative of F(x) = cos is Blank 1 (use fraction form not…

A: ∫cos6(x2)dxsubstitute u=x2→dudx=12→dx=2du=2∫cos6u du=2[cos5u.sinu6+56∫cos4u…

Q: 5. Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0 <0…

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Q: (11 marks] If u(r, y) and e(r, y) are harmonic functions in a domain D, then show that the function…

A: This question is related to Complex Analysis

Q: Q1: Locate the zeroes of the following functions and determine their order. 1) z4 + 10z² +9; 2) z³…

A: Find the zeros of the function and determine the order. 1) The given function is: z4+10z2+9 Factor…