) Suppose f(x, y, z) an iterated integral, √x² + y² + 22 and W is the bottom half of a sphere of radius 6. Enter p as rho, o as phi, and as theta. D [[[ fav - "" [" dV= W dp do de

Q: Let S: x² + y² + z² + ax+by+cz= d be the sphere with radius r= 9 and centre on the z axis, with…

A: The sphere x2+y2+z2+ax+by+cz=d and has a radius 9 and center on the z axis with coordinate zc=4 To…

Q: Prove that  that the y=0 is the horiz.asymp.  and x=-1 and x=1 are vert.asymp, of y=coth-1x through…

A: As given that for the function y=coth-1x has verical asymptotes at x=-1 and x=1 and has horizontal…

Q: 20. Let S be an oriented surface parametrized by r(u,v). Define the notation do = r, du × r, dv so…

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Q: Evaluate the line integral 2 Cx2y)dx- 2xdy along each of the following closed paths, taken…

A: Given that the integral,

Q: Q₁) Find Jz dz 1. along the contour integral c from 1+i directly to 3+i3? 2. along line from 1+i…

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Q: d Fill in the chort: use 3 2 lost 2 coso -) 30° 60° 120 180 240° 2300 3000 230° 160

A: The solution is given below

Q: 1. Check that each given function u is harmonic and if so then find a harmonic conjugate of u. Write…

A: Here as per our answering guidelines we are going to answer of red marked question (g) as follow:

Q: The complex function fla)=ulx.y) + ¿elx.y) Con be differentiated ony point Tin complex opoce The…

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Q: fy the notation that shows the transformation of triangle SML onto triangle S'M'L' to show the…

A: Explanation and solutions is given below....

Q: Calculate the area of the triangle defined by u = (1, 6, 2), v = (3, 0, 5). [A3]

A: Here we have to calculate the area of the triangle having vectors,  u→=(1,6,2) and v→=(3,0,5)

Q: Show that for all values of θ and φ, the point (a sinφcosθ, a sinφsinθ, a cosφ) lies on the sphere…

A: Show that for all values of θ and φ, the point (a sinφcosθ, a sinφsinθ, a cosφ) lies on the sphere…

Q: 4) Let B be a sphere with radius a and center 0 and r be the radial dis- tance. Applying Green's…

A: Consider the provided question, Let B be a sphere with radius a and center 0 and r be the radial…

Q: 5. Find u-dr for a unit square in the first quadrant with vertex at the origin by Stokes's C theorem…

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Q: Let ∆ABC be a triangle. (a) Prove that B’ lies in the interior of AC if and only if ∠BAC and ∠ACB…

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Q: 4. Let C be the unit circle in the xy-plane, and S be the boundary of the square with side 1,…

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Q: ²²-i)² dx 2³+dz when the contour C is the circle |z − 21 = 5 +4 1 Z- COSZ Cosz, dz when the contour…

A: According to the guidelines only three subparts should be answered. Therefore to answer the rest of…

Q: Find all angles between 0 and 2T satisfying the condition -1 Cs x = Separate your answers with…

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Q: If F(x, y, z) = 10yzi + 10xzj + 10xyk, find div F and curl F. div F =

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Q: 1. Find the area of the portion of the plane Зх — Зу + 2 — 12 that lies inside the cylinder y? + 22…

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Q: Calculate the following integral 1 Lc (z − 1) (2³ — 1) dz for each of the following contours C. In…

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Q: 5. Calculate the following integral √e (z − 1) (2³ — 1) -dz for each of the following contours C. In…

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Q: Ifu =x +y²+z², find curl Vu.

A: Solution:-

Q: Compute the two Parbials Of each af the following functions fcaxy)=¢ + 3xy %3D b Z=J x Sin cocy) %3D…

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Q: az If z? = y sin(xy), find ду at the point (-1, ", 1) a) - 0.5 b) +1 c) - 2 d) -- 1 f) 1 e) 0 g)…

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Q: A secant to two congruent circles, which is parallel to the line of centers OO', meets the first…

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Q: Find aw in terms u and v if du w= In(x2+y2 +z²), x = ue" sin u, y = ue' cos u, z = ue"; (u, v) =…

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Q: Which of these is the correct parametrization of the line connecting (1,2,5) and (0,3,– 1)? A. x =…

A: We know that parametrization of the line connecting pointsx1,y1,z1,x2,y2,z2 is given by x=x1+tx2-x1;…

Q: Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

A: Given  that  y→1, y→2, y→3∈ℝ5 and that                   y→1+ y→2+ y→3=0→. and           Y^=spany→1,…

Q: 9/ Find the Vale of the integrel ) Losz+Retz)r Imtz)} dz 3 is the Straitht line Segment from Zero to…

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Q: HW) If rCH)=6 sinzt ċ+ Gcas zt j + 5tk find F,Ñ, V, a and speed at t-2

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Q: Suppose that the Celsius temperature at the point (x,y,z) on the sphere x +y +z = 1 is T= 1100xyz".…

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Q: find alea in bounded and in which Juadiantgon メ-exis lies fist lind Give U-n. where is explession…

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Q: What are the coordinates of point B on AC such that AB is of AC? 3+ 1+ -1 3. -1+ -2- A -3 Choose 1…

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Q: t DR) dende Dartine dövßes e te than show that Deo) X DR1) to DG20). o is atoxphic

A: To show D20×D21 is isomorphic to D420: Define a map f:D20×D21→D420 by fa,b=a×b a×b∈D420: Suppose a…