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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: Find the wark done by the Foree Field FoK x>ye^> along the parabola X=y+1 from (bo) to (2,1).

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Q: Evaluate the following integral 2dr J z (3(In z)2 + 12 In r- 15)

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Q: Exercises Caleulate the following integrals: 2'Gasade 4) de, where c in 2+1 (2-1)(a-2) %3D the two…

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Q: (b) Suppose C is a curve of length N, and ||F|| < M, where M is some positive number. Prove that ·…

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Q: Assume s is a smooth surpace parametrized by e (u,v): <Jv, win' u, SZ-v ). Evaluatk 2x sin y do.

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Q: Evaluate the following integral using Cauchy's integral formula. In which C is the circle |z| = 2

A: AnsGiven C is the circle z=2∮c 2z+1z-idz has singularity zo=iNow ,z=2     z-0=2   centre =0 and…

Q: Let D= ((r,)|isrs2s0s 2n). Sketeh the reqion D, and evaluate the double integral Do r dA.

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Q: Calculate Hhe fourier coeffrecents Of the fancdion fR) over the nderval -スと×L2 here: Fx)=(0,-2くメCー…

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Q: d) ej Z [√2] is a field Z [√2] is an integral domain

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Q: Let C:z|=1 in the counterclockwise direction and I = $. dz, J = f. Lnzdz, and K = $. tanzdz. For…

A: We can apply cauchy Goursat theorem on I and K but not on J

Q: Suppose that h is integrable and that h(r) dr = 0 and L h(r) dr = 6. Find .3 h(r) dr -/ h(u) du a.…

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Q: Compute the double integral of f(x,y) = 20x*y over the given shaded domain in the following Figu 1 1…

A: We can answer question as per the honor policy. Please resubmit other question as well to know the…

Q: Suppose C is a curve of length N, and ||F|| < M, where M is some positive number. Prove that F. dr <…

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Q: Is dz

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Q: Given the force field F (x, y, z) = 1.) Show that SF · dR is independent of path without computing…

A: We know that the line integral of a vector field is path independent if the vector field is…

Q: For each of the given paths, verify Green's Theorem by showing t dA. Also, explain which integral is…

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Q: Fid

A: To find the triple integral ∫∫∫B24xy2z3dV , where B is the box B=0,a×0,b×0,c. dV=dzdydx.

Q: 3. Use the fact that F = is a conservative vector field to evaluate SF. dr when C is the path r(t)…

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Q: Evaluate the following integral using Cauchy's Residue Theorem. z+3 dz. $ |z-51-3 (z − 3)(z - 6) (z…

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Q: Comi der Hhe falßlning. J= x' J = 6-x of the ragan bj intyng awea ef mgount to O Fnd the wi th ayact…

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Q: ofind the Veelles Such that of A ond R

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Q: Use Green's Theorem to evaluate the following integral Sa x²ydx + xy²dy, where C : x² + y? = 4 with…

A: The given integral is: ∫Cx2ydx+xy2dy ;     where C is the boundary of the curve: x2+y2=4

Q: Compute the following integral: ez -dz z(z – 3) where y = {z : |z| = 2} positively oriented.

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Q: Suppose that g: [a, b] → R and h: [c, d] → [a, b]. Prove that if g and h are monotonic then go his…

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Q: Compute the double integral of f(x,y) = 36x³y over the given shaded domain in the following Figure :…

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Q: Prove that o curl f dS = | 6f · dr - v ¢ x f · d$.

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Q: Calculate the middle rectangle approximation of , Vxdx using five subintervals. O M5 = 0.624 M5 =…

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Q: Evaluate the integral o f(z) dz, where C is the unit circle enclosing the ori- C gin, and f(z) = zz.

A: Given-A circle C,which is unit circle enclosing the origin           -f(z)=zz  To find- ∮Cf(z)dz

Q: Let D be the portion of z 2z + 5y inside z+ y 1, oriented up, and let F= (y, z, z).Compute F dr

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Q: Let / = [c, d] [a, b], show that g =xj is Reimann integrable on [a, b] and b. S g(x)dx = d-c a

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Q: 4. Show by defintion that f:R R, f(z) = cos(z), is continuous on R. Hint: you may need to mimick the…

A: 4. In the proof of showing that sinx is continuous we have taken any real number c and we have seen…

Q: If F is a conservative vector field on a region R, how do you evaluate∫C F ⋅ dr, where C is a path…

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Q: Compute algebraically the resultant of the following complanar displacements: 100 N at 30°, 141.4 N…

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Q: Consider f and g in V= CI0,1). with the inner product (.9) given by the integral J«9ac) at. Compute…

A: Let us consider an inner product on a vector space V, defined as   f: V x V→F  where f is v,u The…

Q: Compute The integral f the scalar funetion over r (t)= bxy+32 %3D f(x,yd= ? 3.

A: Given curve is r(t)=cost,sint,tx=cost, y=sint, z=tdxdt2+dydt2+dzdt2=(-sint)2+(cost)2+1=2

Q: Evaluate the following integrals (taken anticlockwise) using Cauchy's theorem: (f) P.„(²+1)² eiz dz…

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Q: Prove that o curl f· dS = f pf • dr - f v o xf - d$ %3D

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Q: Suppose_that a baundlecd tn R with du = o un u = Au on the boundary 20. Show that gran Carel is…

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Q: ate the integral by making the giv dt u = 1 – 6t 7: (1 – 6t)*

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Q: Compute the work done (in J) for a force F = 14 N from x = 1 to x = 2 m.

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Q: T/3 L, S, Srª yz tan xdxdzdy

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Q: Let D be the portion of z = 2z + 5y inside z² + y² = 1, oriented up, and let F = (y, z, -z). Compute…

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Q: Evaluate the following integral fx cotx dx Select one: 1 + 2 Mx-x+C +C None +C 2 cot-x +21+x² +C 2…

A: I am going to solve the given problem by using the integration by parts to get the required result.

Q: Let D be the portion of z = 2x + 5y inside z? + y? = 1, oriented up, and let %3D F (y, z, –2).…

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Q: Let C:/z|=1 in the counterclockwise direction and I = $ Lnzdz, J = $. zdz, and K = $. tanzdz. For…

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Q: Find of the operstor a norm A(x) = S (2.+st)x(t)dt %3D A: C [o,1] →L [o,I] O a. 2 O b. 7/12 O c.…

A: Option (c) is correct.

Q: Prove,J w' Sin wx du %3D COSZ 2

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

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Q: Evaluate the following double integral dydr, -here D is the entire plane

A: The question is taken from the calculus in which we have to find the double integral of given…