2.3 Use the Cauchy integral formulae to evaluate 22 - 1 Jo (9 – 2*)(2 + 2i))" where C is a circle |2 + i| = 3.

Q: 3.1 Use the Cauchy integral formulas to evaluate the eiz cos z -dz, Ie z2(2z – 37) | where C is the…

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Q: 5. Use the binomial expansion and Cauchy's Integral Theorem to evaluate P ( C=10 2n dz where C is…

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Q: 3.1 Use the Cauchy integral formulas to evaluate the eiz cos z *zp- Se z?(2z – 37) where C is the…

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Q: 3.1 Use the Cauchy integral formulas to evaluate the eiz cos z -dz, La 22(2z – 37) where C is the…

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Q: 42. Show that the graph of d ae""cos wi is bounded by y = ae-ct and y = -ae-ct for a > 0 and c> 0.

A: We know that,

Q: 3 Evaluate the integral de using the two-point Gaussian quadrature rule O -|4 1035 N/N N/W 끔

A: We have to evaluate the integral ∫−3311+x4dx by using two-point Gaussian quadrature rule. Here,…

Q: 3.1 Use the Cauchy integral formulas to evaluate the eiz cos z dz, L.7(2z – 37) where C is the…

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Q: 2. Use Cauchy's Integral formula, Evalnate the following. • I= 6 Sin4Z :(Z-4)3 IZ1= 3 I = . tanttz…

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Q: 2.3 Use the Cauchy integral formulae to evaluate 22 – 1 (9 – 22)(z + 2i))3 where C is a circle |z +…

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Q: Calculate the area of the inner loop of r = √3 − 2 cos θ.

A: To Find: Area of the inner loop of r.

Q: The approximation of the integral -2) In (x+2)dr using the two points Gaussian quadrature மாmua is)

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Q: 8 Use the Cauchy integral formulae to evaluate 22 – 1 - (9 – 22)(z + 2i))³ | where C is a circle |z…

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: Evaluate the integral ſſ /ydA, where T- triangle with vertices (1,0), (0, 1), (1, 1).

A: Let us consider the double integral  I=∫ab∫f(x)g(x) f(x,y) dydx    or I=∫ab∫f(y)g(y) f(x,y) dxdy…

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Q: By using the Residue theorem, compute the integral eiz -dz, where I is the circle |2| = 3 traversed…

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Q: 3.1 Use the Cauchy integral formulas to evaluate the e cos z I. 7(2: – 3m) where C is the region…

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Q: Show that the finite difference formula 1 Dzu(î) = [Зи (т) — 4u(г — h) + u(т — 2h)] 2h is a…

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Q: Evaluate the integral (6x-y)dx + (x+6y)dy along the path C, defined as y = 16-x² from (0, 4) (4, 0).…

A: Answer: The solution is given below:

Q: (2,4,2) √(122) Axlna +(By²2)] + (2 +9³) 2² what should A ond & be for the integral to be path…

A: Let us denote F1=Axlnz, F2=By2z and F3=x2z+y3. We have to find the value of A and B such that the…

Q: 1 Use the Cauchy integral formulas to evaluate the e cos z *zp- 22(2: - 37) where C is the region…

A: Given: Let  I =∮C  eiz cos zz2 2z-3π dz  .....1 And,  C is the region covered by circle z-2=3.

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Q: Use the Cauchy integral formulas to evaluate the  ∮c eizcos z/ z2(2z -3π) dz,  where C is the region…

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Q: Find the area +6 C1 R -6 +6 C2: 4x2 + y² = 16 -6 using green's theorem.

A: We are given the above region of which we need to find the area and as per the instruction, we need…

Q: 2.3 Use the Cauchy integral formulae to evaluate 22 -1 J (9 – 2ª)(2 + 2i))* where C is a circle |2 +…

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: 2. Use Cauchy's Integral formula, Evaluate the foll D I - & tantz Z² C: 171=1

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Q: ) Let z be a c complese number then cos ( 58+2) is bounded in C2

A: Since, sinz and cosz are unbounded on C. These are unbounded along horizontal axis .

Q: Find the product of the integral 1- S x²cos(xy)dxdy

A: We have to change order of integration first.

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Q: Evaluate the integral S 3012 2/3 de using the two-point Gaussian quadrature rule. 1+16z4

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Q: 1.6 Compute the integral 2) Jyez dz where is the line segment from O to Zo

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Q: show that the. fallowing Complex functron is dis continuous at z=? 121 1 fCZ) = スー! %3D 3. %3D

A: Topic:- limit and continuity

Q: Consider the following integral 3d.r (16-472)5 A suitable trigonometrie substitution to reduce it to…

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Q: Find the areas of the regions Inside one loop of the lemniscate r2 = 4 sin 2θ

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Q: 1- Find the integral of: 2 cot - de 3 7/2 A- B- dr Vr

A: (A) Given integration is : ∫π2π2cotθ3dθ Use property of integration ∫cotaxdx=logsinaxa+c

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A: Solve the given problem.

Q: 1 2 Compute R dA where Ris the region above.

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Q: 4. Find path integral J xdx+ ydy, if L is the segment: x-1,y= and re (0.1]

A: Given x=t, y=t2, t∈0,1

Q: Can i get help step by step with this problem?

A: Given:

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Q: Evaluate the Integrals using cavely's in tegmal formula s 1 $(2) = dz where e is the eivek (8-x)…

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Q: Prove the following: 7. Given: PS bisects ZRST, 2SP = 3SQ, 2ST = 3SR T. Prove: ASTP~ASRQ

A: topic - similar triangles

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Q: 37. Evaluate the integral fи 4x³y dx + x* dy for any closed path C.

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Q: determine the area inside of the inner loop of the limaçon r = 2 cos 0 – 1.

A: We have to find area of r= 2cos(theta)-1