Let C:z|=1 in the counterclockwise direction and I = $. Lnzdz, J = $. zdz, and K = %3D $. cotzdz. For which integral(s) can we apply Cauchy Goursat theorem? For I and K only For I, J, and K For I only None of these O For K only

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Q: Evaluate the given line integral. | (y, -x) · dR, where C consists of the uppder part of x2 + y? = 1…

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Q: 2- Assume that x, y € R and z = x + iy e C and answer the followings. Calculate the reel integrals…

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Q: Let C:z-1 in the counterclockwise direction and /= Lnzdz, J $. zdz, and K = %3D . cotzdz. For which…

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Q: Let C:z|=1 in the counterclockwise direction and I = 4. Lnzdz, J = $, zdz, and K = $. tanzdz. For…

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Q: Let C:z–1 in the counterclockwise direction and I = 4. Lnzdz. J = §. ždz, and K = tanzdz. For which…

A: For K only

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Q: Rewrite the iterated integrals in the order dzdydx 11-y? 1-y SS S f(x,y, z)dædzdy So So" o f(z, y,…

A: Please refer to the image below

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Q: What is the value of the closed integral cos(iTiz)/z with respect to z within the closed circle /z/…

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Q: Let C:z-1 in the counterclockwise direction and I=6 Lnzdz. J .dz, and %3D %3D 2+5i K tanzdz. For…

A: Cauchy goursat theorem is applicable to analytic/holomorphic functions. If a function F is analytic…

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

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

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Q: Verify Green's Theorem by evaluating both integrals aN v? dx + x² dy | dA ду ax for the given path.…

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

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 5…

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Q: FOR R U ARI ABLES TO CALCULATE THIS INTEGRAL OF wiHEREis THE EIGHTH OF A SPHERE În OCT ANT I,

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Q: Let C:z-1 in the counterclockwise direction and I= $dz, J = . Lnzdz, and z+5L K = 6 tanzdz. For…

A: Cauchy Gourast theorem: Suppose that function 'f' is analytic in simply connected domain D, then…

Q: Evaluate the triple integral. SIJE3Y dV, where E is bounded by the planes x = 0, y = 0, : = 0, and…

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Q: By inversion of order, the integral 23 zy dy dz is equivalent to 3 3z/2 ry dz dy OJ. S ry da dy 3y…

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Q: Suppose f(x,y,z) = and W is V² +y² +z? the bottom half of a sphere of radius 5. Enter p as rho, o as…

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Q: 3. Evaluate the integral cosh ™z dz, z(z? + 1) Izl=2 where the circle |z| = 2 is described in the…

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Q: Compute the contour integral dz, where l'is the contour of the perimeter of the square with vertices…

A: We will do it  by dividing r into 4 paths.

Q: Let C:z-1 in the counterclockwise direction and/- dz, J = $ Lnzdz, and K-4, tanždz For which…

A: We are asked to find where the Cauchy Goursat theorem applicable. So, first we state the Cauchy…

Q: Let C:z|=1 in the counterclockwise direction and I = $. Lnzdz, J = §. zdz, and K = %3D $, tanzdz.…

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Q: Let C:z|=1 in the counterclockwise direction and I = 4, Lnzdz, J = f, zdz, and K = %3D %3D $.…

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Q: evaluate the contour integral z^2 -z^4/z-1)cos(z)where c:|z|=4

A: Introduction: Cauchy's integral formula is very significant in complex analysis. It helps to…

Q: Let C:/z|=1 in the counterclockwise direction and I = $. Lnzdz, J = f. zdz, and K = %3D $. cotzdz.…

A: We apply Cauchy Gaursat Theorem on the given questions. For complete solution kindly see the below…

Q: Evaluate the line integral ScF- dr where F(x, y) = (5x + 4y)i + 3xyj and C: r(t) = 3ri + rj, 0sts1 O…

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Q: Evaluate the given line integral. | (y, –x) · dR, where C consists of the uppder part of x² + y? = 1…

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Q: Let C:z=1 in the counterclockwise direction and I = . dz, ] = f. Lnzdz, and z+5 K = $, tanzdz. For…

A: Here we will check whether the function is analytic on given region, And then will decide the…

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

A: For K only.

Q: Use Green's Theorem to evaluate the integral |x?ydx + xydy where Cis the rectangle with vertices (0,…

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Q: Evaluate the given integral using the Cauchy Integral Formula or theorem. z2 +1 dz z - 2 | where y…

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Q: which of the sets is orthvoonal under the given inner product on C[0, T] ? = S fusgıx) dx I. {1,…

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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: Let C:zl-1 in the counterelockwise direction and I = 4, Lnzdz, J = , ždz, and K - $, tanzdz. For…

A: Last optiom is correct  That for only k we can apply cauchy goursat theorem

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…