6e? Evaluate dz by residue theorem, 9z4 + 45z3 where C'is the contour z = 2

Q: H.W: Use the Trapezoidal Rule with n=6 to approximate. Here f(x}=sin2x,a=0,b=x.

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Q: 4. Let w = f (z) = 2iz + 67, find u and y and the value of f at z =+ 4i %3D %3D Z ==+

A: We need to find u, v and value of f at z.

Q: e*, when 20 = -1 %3D P„(x) sin(nrx) – nn cos(nax), when 2, = (nx)² for n = 1,2,3,.... a.) Show that…

A: Hi! As the questions are lengthy, we are answering only the first subpart. If you need an answer to…

Q: 2. Find an upper bound of the absolute value of the integral e + 1 (a) dz, where C is the right half…

A: We know that : Imz=12z-zi . Therefore, ∫Cz2-Im(z)dz=∫02+2iz2-i2z-zdz.

Q: 5) Compute J(x²+y?)dxdy, where D is the intersection of c irc les r=2 cosg and =2sing.

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Q: Evaluate ∭E sqrt(x2+y2) dV where E is the region that lies inside the cylinder x2+y2=4 and between…

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Q: Q:Ifx = sin 6, y = 0,y= cos p6, prove that (1-x )y, xy,+ p°y= 0, dy and y1 d dy where y, %3! %3! de

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Q: By using the residue theorem, prove that 1 dx 4a3 where x E R, and a >0 is a parameter.

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Q: Q4) Using Green's theorem to evaluate: (12 marks) Sc [ (x3 – xy³)dx + (y³ – 2xy) dy] Where C is the…

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Q: Let y be a line segment from z = 2i to z=7+2i. What is the value of the integral fs (2 )dz , where f…

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Q: Integrate counterclockwise dz by Cauchy's formula z2 – 16 counterclockwise around the circle C : |z…

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Q: Evaluate I 8z(2r? + y) cos(4.r* – y*)dzdy where R is the region above y 2r2, below y = -2r2, and…

A: We want to evaluate ∬R8x(2x2+y) cos(4x4-y2) dxdy over the region R, where R is region above y=2x2…

Q: Numerically integrate f(x) = x2 from a=0 to b= 2 using a multiple segment (n-2) trapezoidal %3D…

A: Trapezoidal rule  ∫abf(x)dx≈Δx2​(f(x0​)+2f(x1​)+2f(x2)+2f(x3​)+⋯+2f(xn-1​)+f(xn​))whereΔx=b-an

Q: Wz bisects LXZY and X = LY. Which choice of method can be used to prove 4XWZ = AYWZ? O sS O AAA O…

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Q: Q6. Let w = f(r,0), r = √x' + y³, 0 = tan'(y/x), ), find aw ?х > and ди ду in terms of r and 0.

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Q: Let f (z) = x² + iy? where x and y are the real and imaginary parts, respectively of z and C is a…

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Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 - y³)żdy

A: Given integral ∫b2y6-y812dy The objective is to evaluate the integral by trigonometric substitution.

Q: C. If w=f(x,y) and x = r. cose, y=r. sine. Prove that aw ar aw +1 (2001) = fx² + fy²

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Q: 4. a. Find zx + Zy: given that z(x, y) = tan(x3-3x?y2+2y4) V9-х2-у? b. If u then show that x ди дх…

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Q: (Q.)AUSE T.cx)-1 ad Tilx)= X, t fnd TECK) nd 万(x) (b) Find the raats of Ti(K) nd Tiw using the…

A: a) Given that, T0x=1 and T1x=x. Note that, the powers of x as function of Tnx for x2=12T0+T2 and…

Q: The path integral v- dr, where v = (sin y, x - cos y) and C is the perimeter of the triangle formed…

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Q: given sin -In\x+ y + 19| Ax, y) = V18 – (x + 11)² – (y + 10)² sketch domain p(-11+ v7, - 10) is…

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Q: dx, Simpiny the dls ver using nyper ons. Select the corr oice. 2x 1 +C O None of these. 2+1 + C 2 O-…

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Q: Find F. dr for F = 4yi + 2x j - 2z k if C is the helix x = cos t, y = sin t, z = t, for 0 <t < 4n.

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Q: B) Find (블)x,()'(일), Prthe Pte 2- w= x?+y-2 +sin z 3. w:x+y+2", ysinz+ z sin so

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 10.18. Use an appropriate change of variables to evaluate the integral ff,(1 + x? + y²)²dA, where T…

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Q: EX: Show that o dz =2TL whcre CIS a unit Circle. Sal: Z= re. io dz = ire do ig ir e de %3D = 2i Note…

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Q: (d) Let 0 arg(z). Take C to be the wavy contour in the z-plane described by 0 < arg(z) < T; |2| =1-…

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Q: Show that u(x, y) is harmonic in some domain and find a harmonic conjugate v(x, y) (7 Marks) When:…

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Q: Q2. Evaluate $. dz where C is: (z2+1) cosnz Ay 3/2 1. Iz – 2i| = 0.5 2. %3D -1 1 x |-1/2

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Q: z+y? for F (x, y, 2) = ( ?y° z, Va + y+ z, at the point (1, 1, 1) find the exact answer (on the…

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Q: Q1: - Find Ow/Du and Əw/Əv if w- xy + yz + xz ,x-utv, yru-v,z-uv at the point (u,v)- (0.5,1) (30…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: a²f If f(x,y) = e" sin (r + y), then prove that дхду дудх %3D

A: Hi! You have posted two non-related subparts. As nothing is specified, we are answering only the…

Q: (b) Apply the method of contour integration to prove that (2m de 2n Jo 2+cose 3

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Q: af ar fe Consider f(1, y, z) = r² + y²z² and I=r sin 0, y =r cos 0, z = Or³. Find and

A: The function fx,y,z=x2+y2z2 and the polar transformation coordinates are x=rsinθ, x=rcosθ and z=θr3.…

Q: W z bisects XZY and 2X LY. Which choice of method can be used to prove 4XWZ AYWZ? O ss O AAA O SAS O…

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Q: Find b∈R such that ∫∫Ssin (b) ydS = 8, where S is the part of y^2 + z^2 = 4 that is between x = 0…

A: To find the value of b satisfying the given integral.

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+a?)2 dx = By using the residue theorem, prove that 1 dx where x E R, and a > 0 is a parameter.

A: Using the residue theorem we have to prove..

Q: the Area that lies inside r=3+2 sin 0 out side r=2 is -24.187 -23.957 23.957 24.187 24.315 Evaluate…

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Q: Q4 Find az when u = 0,v = 0 du If z = sin xy + xsiny, x = u2 + v² ,y = uv

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Q: Let f (z) = x² + iywhere æ and y are the real and imaginary parts, respectively of z and C is a…

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Q: (b) Given  = (x²y)î + (xz – z²)f – (xyz)k, determine the following at point (1, 1, 2): (i) V- Â.…

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Q: 2.1 Evaluate la Im(z – i)dz where C is the contour from z = 1+ 2i to z = i and from z = i to z = -i.…

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Q: Q5: Find W,e if W = f(x,y), xr cos6 and y =r sino, then prove that r Wre =-yf + xfy+ xy(fyy-fex) +…

A: The given problem is to find the double partial derivative of the given multi variable function and…

Q: z + 16 f (2) = (z – 3) (z – 16)? Let C be the circle |2| = 9, in the anti-clockwise direction.…

A: It is given that the complex function is fz=z+16z-3z-162. We have to find the residue of fz at z=3…

Q: We have r(t) = (2e-t, sin-'t, In(1 –t)) , %3D Find 1- The domain 2- ar , an, T, N and t at t=1

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Q: 19.22. Find the value of the integral Sc[(z + 2)/2] dz, where C is: (a) the semicircle z = 2e", for…

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