2 sin 50 do. 9. Use the residues' theorem to evaluate sin o

Q: 4.3 Use the calculus of residues to evaluate the following integral 27 1 do. 1+8 cos? 0

A: Note:-  cosθ=eiθ-e-iθ2 Residue Theorem:- ∫Dfz dz =2πi ∑k Res fzk=2πi×sum of residues   Given that…

Q: a) Show that U = e-x sin (nt) is a solution to a²u = 0. %3D ax2 at2

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Q: 7. Evaluate using the residue theorem eir dx x2 +1

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Q: Find the Taylv the Taylov for>fa)-sinr i vend series

A: Given

Q: Find the length of the path for c(t) = (4(0 – sin(0)), 4(1 – cos(8))) over the interval 0 < 0 < 2r.…

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Q: Find the area of the region shared by the cardioids r= 12(1+ cos 0) and r= 12(1- cos 0). The area…

A: General equation of the cardioids is r=a(1+cosθ) and Area of the cardioids is 6πa2

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

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

Q: 4.3 Use the calculus of residues to evaluate the following integral r27 1 1+8 cos? 0

A: We find the given integral by using calculus of residues.

Q: tan z, + tanz, = T-(tan z;) +(tan 72) tan(z, +2) ) Prove that: cos(z + w) = cosz cosw + sinz sin w

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Q: (a) The averages of cos x and lcos x| from 0 to x are (b) The average of the numbers v,, the average…

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Q: Find the Re(z) and Im(z) z=sin(e^i3)+sinh(5∠30)

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Q: Find all the singularities of tan(z) f(2) = determine their types, and compute the residues at the…

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Q: =: Evaluate sin (A) using: Let A (a) Caley-Hamilton method.

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Q: 27 de Evaluate the intergal using the residue theorem. 12 + 6 sin e

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Q: 91. Let I, = | x" cos(x³) dx and J, = | x" sin(x²)dx. (a) Find a reduction formula that expresses I,…

A: We have to find a recursive / reduction formula for the given integral.

Q: Reduce to the form a + bi: a. sin (2 – i); b. cosh (1+ i).

A: Given: sin2-i cosh1+i To do: Reduce the given into the form a+bi.

Q: •2n Let a and b be distinct nonnegative integer. Prove that Sa sinax cos bx dx = 0 %3D

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

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Q: 2-Consider the function defined by the base i) Find dz (ii) Prove that x дz ?x - дz ду z =…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Use symmetry to evaluate the followingintegrals.

A: We have to find definite  integral using symmetry.

Q: 2. Evaluate J dx x²√√x²-49) x>7, using a trigonometric substitution.

A: NOTE: Refresh your page if you can't see any equations. . ................(1) substitute  take…

Q: e sin z -I lim z+0 16 cos z – 16 (Us

A: From the given problem: limx→0exsinx-x16cosx-16 Now solve:…

Q: 9. Using n= 8 approximate the value of cos(1+Vx )dx using (a) the Midpoint Rule, (b) the Trapezoid…

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Q: de Evaluate the intergal using the residue theorem. 13 +4 sin e

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Q: b) Find the common area between r= 4 cos (0) and %3D r=2 sin (0).

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Q: The area between the two loops of the limacon r = 1 + 2 sin 0.

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Q: Evaluate the principal value of sin(3 + j4) O a. none of the above O b. 2.51 - j2.31 O c.2.31 +…

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Q: 14. Find a) esin 2xdxb) J vanyt dx, using the substitution x= 2 tane. 15, Find a) fxe"-dx b) dx…

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Q: tan? z sec? x + sec a Prove 1-cos I

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Q: nd the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form…

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Q: Find the residue of f(z) = (1 – 26) sin(1/2).

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Q: 2. Find the area enclosed by T = @ cos 30-

A: We need to find area.

Q: sin 7Z „Find the residue of f (z)at z = 4 (z – 4)? Let f (z) =

A: Note:

Q: 1. Show that f(r) = sin(r + 3r) is equal to g(r) = -I Cos(I) at least once on -l. Hint: Think about…

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Q: do Evaluate the intergal using the residue theorem. 12 +1 cos 0

A: ∫02πdθ12+1 cosθLet, z=eiθ . Then cosθ=(z+z-1)/2, dz=iz dθ, so that∫02πdθ12+1…

Q: Ifcesese - sin e = t and sece - cos e = m. prove that 1'm? (12+ m? +3) =1

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Q: 4.3 Use the calculus of residues to evaluate the following integral 27 1 1+8 cos? 0

A: We have to solve the integral by residue formula

Q: Q:9 Evaluate cot(72)\dz 3 [z e? + by Cauchy's residue theorem.

A: We have to solve the given integral by Cauchy residue theorem

Q: Find all the singularities of tan(z) f(z) = determine their types, and compute the residues at the…

A: Given function is fz=tanzz. We have to find the singularity of fz. Now, limz→0fz=limz→0tanzz00…

Q: 2 de Evaluate the intergal using the residue theorem. 12 + 6 sin 0

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Q: - Using Euler's equation, show that- : z fain (K 0)} - z sin Ø z2 – 2zCos Ø +1

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Q: 21. Evaluate ſ dx by using Residue theorem. 2+x4

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Q: Use the Product Rule to compute fx and Sy for f(x, y) = 2xye" sin (y). (Give exact answers. Use…

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Q: The area between the two loops of the limacon r = 1+2 sin 0.

A: Question- The area between the two loops of the limacon          r = 1 + 2  sin theta .

Q: 27 de Evaluate the intergal using the residue theorem. 13 +4 sin 0

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Q: 4.3 Use the calculus of residues to evaluate the following integral 2 1 1+8 cos? 0

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Q: (d) Using your answer to part (c) compute h'" (x) where h(æ) = 1/ cos(x) and a is such that cos(æ) #…

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Q: 1 Find Maclaurin polynomial P, to ƒ (x )= 1 1 sin Ax cosx 1-x 1+x

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Q: (1) Given that z = 1-iV3, express z in the form r(cos e + i sin e) Hence write down z7 the form

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Q: using finite Fourier tran form, solve du given ulo,t) =0, U(4,) =0 and u(x, 0) = 2% -2X where o<x…

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