Use the residue Theorem to show that T Cosh 7 2 sinh 7' 2 sinh² 7. 22 -1 -dz 3Di Se (22 + n²)² sin z around the circle C with equation |z – i| = 3. Hint: sin(iz) = i sinh z and cos(iz) = cosh(z).

Q: If u = x² cosy+ ye", where x = s+2t and y = st, prove that ди ди 2- (s – 21) (x siny- xye – e"). -…

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Q: 3 e flow in the field F = 4i + 9j + 2k along the path C, where C is the curve r(t) = 7 cos 4ti + 7…

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Q: Q2= A) for E= 2xĭ-3Y3+K %3D prove That divc curl È)=0 %3D

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Q: ON REDMI Y3 AL CAMERA - veifhy coucly's is Theorem for the function C) 3 Cosh(z+2 where C is the…

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Q: Let r(1) = (sin(t), cos(1), 2 sin(t) + 2 cos(21)). Find the projection of r(t) onto the xz-plane for…

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Q: -W : By the same way, prove that g Z sinWo sinw.k Z -27 cus Wo +1

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Q: 5. On the rectangle 0 < x < n, 0 < y< 1, show that |sin z| is maximal at the point z = 5 + i. (Hint:…

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Q: z2-1 What is residue of f (z) = at z=3 ? %3D None -8 Res (f(z),3) = 3 %3D 8. Res (f(z),3) = %3D 8.…

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

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Q: Let C be the shortest path that connects z to mi and /= . (sinhz + 1)dz. Then |=-1-cosh t+ n(1-1)…

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Q: tan-i z = ÷In 1-ja sinh-1z = In(z + vz2 + 1) cosh-1 z = In(z + vz² – 1)

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Q: Which of the following is true about I = f. -2i+3e2z dz? (z+7i)8 I=0 by Cauchy Integral Formula…

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Q: Determine Taylor's formula of order 1 and center a = (0, 0) of f(x)=ex1sin(x2).

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Q: Use the Residue Theorem to find the following (a) ez dz 22 – 1 J]z-1|=1 (b) e dz Izl=42 22 – 1

A: *concept:- Residue theorem.

Q: التاريخ اليوم موضوع الدرس A) Discuss the conrergence of facx) %3D on A = Co,0)

A: Convergence of the sequence

Q: 8.Consider the Bessel equation of order ν x2y′′+xy′+(x2−ν2)y=0,x&gt;0 where ν is real and…

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Q: Express the following to rectangular form. 1. z = v17(cos346° + isin346°)

A: Rectangular form of complex number is defined as z=x+iy Now simplify the given complex number to…

Q: Use the residue Theorem to show that -1 T Cosh T 生 2 sinh T Je (22 + 7²)² sin z 2 sinh around the…

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Q: Use the Chain Rule to find az/as and az/at. sin(0) cos(p), 0 = st7, p = s³t əz t³cos(p) cos(0) —…

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

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Q: Evaluate the integral e-22²+(1-5/)z- 1+] where dz, Cis the (z-1(2+1) circle z =2 traversed…

A: To find the integral of the given function, calculate the residue of the function. First find the…

Q: ax² + bx+c, g(x) = -ax² + bx+c, where ac # 0, th hat f(x) g(x)=0 has at least two rool roots

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Q: d the area of the surface generated by revolving the curve x =cos (2t), y = 7+ sin ( 2° - xis. .....…

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Q: 4. Evaluate the line integral f x siny dx + y dy, where C is the arc of r(t) = ti + t²j from point…

A: Line integral

Q: ) Let Z= re q iy be a complex mumber Such that cosh Z+o. then Re (tanh z) is equal to Sin a cesn

A: In the given question we have to find the real part of tanhz and and also check it that is it equal…

Q: Let C be the shortest path that connects a to ni and I = fe (sinhz + 1)dz. Then None of these…

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Q: Find the second-order Taylor formula for f(x, y) = 8 sin(xy) + 3 cos(xy) at (0, 0). (Use symbolic…

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Q: x²2x+2-5n/x) Sin/2 Sesier. Find the Taylor Centered at 9=1 (x)

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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: 2. Find a closet rank-1 approximation in the f norm to A = cos 8 - sin e sin e cos 0

A: According to the given information it is required to find closet rank-1 approximation in the l2 norm…

Q: (b) If u =x cosy+ ye», where x=s+2 and y= st, prove that 2- ds du - (s - 21) (* siny-xye -e").

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Q: S-) Find the gereral solufon of Sin'x y"- (2sinx.cos x)g'+ Ccosx+1)y = Sih? x given that y-sihx and…

A: Given differential equation is sin2xy"-2sinxcosxy'+cos2x+1y=sin3x Here, qx=sin3x Given that y1=sinx…

Q: The integral of the right hand member of the first order LDE A B C с D -2sin³0 3 COS 2 2sin³0 3 sin…

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Q: 1)the f a) 3 cosh z b) 0 c) in d) n -dz by using the residues is equal to

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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: 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: Let z= 28x + 32xy - 8y , where x(t,s) = cosh (4t) cos (5s) and y(t,s) = sinh (4t) sin (5s). ze at…

A: Here, z=28x2+32xy-8y2

Q: Prove that dz 7-9 (2-2)"dz =0 b,ony integer # -I 2. And Evaluate WHER E Ĉ is the are of the cycloid…

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Q: Evaluate the improper intergal 1 drusing the residue theorem. (x² + 16)?

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Q: Find the residues of the following functions at the indicated points. 2-2 a. at z = 0; at z = 1 b.…

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Q: Use the Residue to Show that the following: 2n de 2n 1+B sin 0 /1– B² Where 0 < B<1

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Q: |1) Use a sine expansion to compute the solution of ( ди д'и at ôx? u(0,t)=u(1,t) = 0,t > 0, u(x,0)…

A: According to the given information, it is required to compute the solution of the given equations.

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: Let f(2)= = csc(TZ) 22 Determine all isolated singularities off and find the residue at each…

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Q: 2) Find the 3 Taylor pelynomial P,(x) of fix) = Sinx at X = * ½

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Q: Let C be the shortest path that connects a to zi and =J. (coshz - 1)dz. Then I=0 |=-sinh n+ n(1-i)…

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