Evaluate . In z dz, where c is |z| = 1 zG-z).

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A: integration by substitution method

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Q: Evaluate the iterated integral | dydx. а. 2 b. 1 с. 0 d. 3 О а. O b. O d.

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Q: What is the domain of: f(x, y) = cos(yv/æ? + 1) O A. D; = {(x, 9)| zy 2 1} OB. D,= {(z,y)이죠, y € R}…

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Q: Let h(y) = In(y In y). Find h' (y). Show your work.

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Q: 10. If f(z). g(z) is integrable on [a, b). prove that (z)g(x)dx f(z)dx g(x)dr.

A: Given that, f(x),g(x) are integrable on [a,b]. The aim is to show that…

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A:

Q: Evaluate the integral / cos[3 +1/(z – 3)] dz, where Y is the unit square with corners at 0, 1, 1+i e…

A: Given; ∫γcos3+1z-3dz Where, γ is the unit square with corners at 0,1,1+i e i

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A: we have to find the value of A.

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Q: Study the analytically of w = L_r(z) at the points z = 0, z = v2,z = -2i

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Q: 2. Use Stokes' Theorem to evaluate S:z=√√√9-x² fF.dr F.dr for F(x, y, z)=5yi-zj+3xk and C

A:

Q: Show that under the assumptions of normal multipleregression analysis(a) E(Bˆ i) = βi for i = 0, 1,…

A: I have solved this question,taking the number of covariates as p instead of k and cov(Bˆ i, Bˆ j) =…

Q: Use Stokes's Theorem to evaluate F dr, where F(x, y, z) = x²i+z²j-xyzk and S is z = /169-x -y . Use…

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Q: b)S godx=? glx)dx=? ラg

A: To find the integrations

Q: e? The singular points of f (z) = that lies inside |z| are z(z²-1) 2 a. 1, –1 Ob. 0, –1 Ос. 0, 1 d.

A: We have to find the singular points of f(z) = ( ez / z(z2 - 1) ). that lies inside | z | = 1/2 are

Q: a) Evaluate ff, (3 – 4x)dV where E is the region below z = 4 – xy and above the region in xy – plane…

A: To evaluate the given triple integral.

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

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Q: { e, a| 1, The Fourier integral of f (x) = %3D A) roo w sin w-cOS w sin zwdw w2 roo sin w-CoS W sin…

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Q: find the indicated extrema, assuming that x, y, and z ar = xyz z - 12 = 0

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Q: Find Vf at the given point. f(x,y,z) = x3 + y2 – 3z2 +z In x, (1,2,4) Vil(1,2,4) =Di+j + ()k ( %3D

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Q: 2. Evaluate the given line integral, (x – y, y) · dR, where C is the line segment from (0, 1) to…

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Q: Let f(x, y) = xcosy-y e*y. fry at (1,0)is equal to: %3D 1

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Q: Apply Green's Theorem to evaluate the integral (4y² dx + 4x² dy), where C is the triangle bounded by…

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Q: Let h (z) = fi v (2t) dt.Find h' (1). Show the computations that lead to %3D your answer.

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Q: Evaluate the integral. | (sec?(t) i + t(t2 + 1)3 j + t6 In(t) k) dt 34 i tan (t) + j 8. + k 4 49

A:

Q: The value of the integral dz , 2 - 3 over the Contour C |2 – 2| = 2 is equal

A: Complex integration

Q: #1. Evaluate the triple integral xy*av, xy?dV, B where B is given by B = {(x,y,z): 2 <x< 3, -1< y <…

A:

Q: Consider the function f (x,y) = x3y3 + xty. Show that it is homogeneous of %3D degree 5 and verify :…

A: A function f(x, y) is said to be a homogeneous function if f(λx, λy)=λnf(x, y) where λ is a constant…

Q: 5. Evaluate z dV, where E is bounded by the cylinder y? + z2 = 9 and the planes x = 0, y = 3x, and z…

A:

Q: The independent variables X and Y are defined by f(x) = 4ax ; 0 SxSr f (y) 4by; 0 SySs = 0,…

A: Answer: Using the given data,

Q: 5. Evaluate the integral yze" dV; where D = {(x, y, z) : –1 <x < 1, -2 < y < 2, -3 < z < 3}.

A: That's easy. Thumb up. Have a good day!!!

Q: Transform the equation ryda (x + 2) dy = 0 into the form of a variable separable f (x) dæ + g(y) dy…

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Q: Evaluate by Cauchy’s integral formula: ∫ c e3z/(z+2)4dz where c: mode z = 4.

A: To find - Evaluate by Cauchy's Integral formula : ∫Ce3zz + 24 dz where C : z = 4     Formula used -…

Q: Evaluate the integral. | (sec?(t) i + t(t² + 1)5 j + t* In(t) k) dt 5 1 tan ti + 12 ,(2+1)j+(등교(1) 1…

A:

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

A:

Q: II. Let f(x, y, z) = z° sin a + Determine 2 dydzərəz'

A: We know, ∂2f∂y∂x=∂∂y∂f∂x

Q: 3. Evaluate the integral o f(z) dz, where C is the unit circle enclosing the ori- gin, and f(z) = 1+…

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Q: the orthogonal trajectories of r = a sin? 0 where a be the arbitrary constant

A: Orthogonal trajectory

Q: Use Stokes's Theorem to evaluate F dr, where F(x, y, z) = x²i+z²j-xyzk and S is z = /169-x² -y² .…

A: As per our guideline we can't use any computer algebra. I calculate both line integral and surface…

Q: h(r, y) = h(0,0) = 0 3x2 + y2 (i) Prove that |h(r, y)| <ly

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Q: cln s Evaluate the integral: St² főr teu du ds dt

A:

Q: Evaluate the integral. (sec?(t) i + t(t? + 1)5 j + t4 In(t) k) dt + C

A:

Q: (a) Show that y = x* is concave upwards at the origin and y= e* is everywhere concave upwards.

A: