A Compute the following contour integrals and give reasoning. 2z dz where C is the positively oriented circle of radius 3, z| = 3. Jc z²(z +4)

Q: Q3: Evaluate z + 1 $c (z6 + 5z5 + 4z¹) (z + 4) dz where C is the circle |z1| = 5

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Q: Find the shortest distance r1 between the two lines given by r₁ (t) = (3 + t, 3t, 5 – 4t) and r₂ (t)…

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Q: 7. Let C be the portion of the circle x² + y² = 4 from (2,0) to (0, 2) traced counterclockwise. (a)…

A: We know if y=f(t) and x=g(t) then mass of the wire of an arc (f(t),g(t)) in a≤t≤b is given by…

Q: Find the midpoint between the two points (3, 6) and (-4, 8).

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Q: Let P = (0,0, 0), Q = (1, –1, –2), R = (2,1, 1). Find the area of the triangle PQR. area = Let T =…

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Q: (ii) (iii) dz c (z²+4)³ where C is the circle |z-i=2 (z-1)dz (z+1)²(z-2)' 1- where C is the circle…

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Q: 2. Find the area of the plane figure bounded by the curves. Plot the graphs of the given functions,…

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Q: 31 Find the exect ares o the sufa ce she O ob tained by votedine the arve about phe rotetigo x axisé…

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Q: Look at quadrilateral WXZY, shown below. isty al T TAT Quadrilateral WXZY is translated 3 units to…

A: quadrilateral XYWZ is given in the figure, we have to find its coordinate points after transform 3…

Q: 30.) Show all steps to evaluate by hand: dA where R (rectangle) –1 < x < 1 and 0 < y < 3 y2+1

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Q: QUESTION 13 Let F(x,y,z)=x²zi+yj-xz²k Find the curl of F. O a-1 Ob.1 Oc_x²-2² Od. x² + z² O ex² - 2²…

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Q: Find the point on the sphere x? + y² + z² = 3 farthest from the point (-6, 6, –6). Farthest point is

A: Given equation of the sphere, Given point is (-6, 6, -6). Distance of the point (-6, 6, -6) from…

Q: - 2+ 7x + 4y that lies inside the cylinder Find the surface area of the part of the plane z = x² +…

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Q: Evaluate zdæ + zædy + (z + y)dz where C is the line segment from (2, 2, 1) to (– 1, 0, – 2). | Check…

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Q: * Nicole Joseph 章《 10 Draw a circle around the ball using the 66 standard form of a circle. A (x-h)…

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Q: Compute с -ater-clockwise see from above. where xdy - y dx ус is the unit circle center at origin…

A: Introduction: In vector calculus, another very important theorem is Green's theorem. It makes a…

Q: Find the length of the chord of contact with respect to the point on the director circle of circle…

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Q: In a Geometry class, Rosalie draws two circles on the coordinate grid as shown. She asks her…

A: Here we have to determine the correct possible responses of her students.

Q: There is a line through the origin that divides the region bounded by the parabola y = 3x – 4x² and…

A: we have been given the parabola y=3x-4x2 to find the points put 3x-4x2=0⇒x(3-4x)=0⇒x=0, 34…

Q: 15. Triangle PQR has the following coordinates. Where is Q' after a translation 9 units right and 11…

A: Given- Triangle PQR has the following coordinates, P-9,-12  , Q-6,-13,  R-7,-4. To Find- The…

Q: Given P (8, 0) and Q (0, -6). The perpendicular bisector of PQ meets the axis of the axis at A and…

A: The points are P(8,0) and Q(0,-6)

Q: 1. Let F = (vi-x)/(x² + y²), evaluate § ♬ dr, where C is circle (x − 1)² + (y − 1)² = r² with 0 <r…

A: We are given that          F = (y i - x j)/(x2 + y2)   Now, r = x i + y j       =&gt; dr = dx i + dy…

Q: 2. Find an equation for the line through the point P(1, 0, -3) and perpendicular xy-plane. to the

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Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

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Q: + 4z 53. Use (7.8) to evaluate dz around the circle |z – 2i| = 2. - z4 + 8z2 + 16

A: Given,  ∮z3+4zz4+8z2+16 dz  around the circle z-2i=2

Q: Find curlF for F = xyz?i+ x*yz?j+ x*y?zk.

A: Given, F→=xyz2i→+x4yz2j→+x4y2zk→ Used formulas, ∂∂xxn=nxn-1

Q: i fc 78 8 Evaluate dz, where C is the circle |z+ 7i| = 8+6, 0<0< 27 z+7i (z+78)"

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Q: Find [2² x²z ds, where C is the line segment from (0,3,-3) to (-5,1,-9)

A: ∫Cx2z ds C is the line segment from 0,3,-3 to -5,1,-9

Q: Show by elimination that x = and y = almost represent the unit 2t2 + 2t + 1 2t2 + 2t + 1 circle x? +…

A: x =2t+12t2+2t+1, y=2t2+2t2t2+2t+1 ....(1)x2+y2=1 ...(2)put (1) in…

Q: 7. Find the distance between the origin and the line (x, y, z) = (-1,3,1)+ t(-1,-1,0). Hint: This…

A: Solution:

Q: Find the distance from the point (1,-7,-8) to the yz-plane.

A: The point .To find the distance between the point and the yz-plane.