23 + 3 4. Evaluate the integral dz, where C is the circle (a) |z + 3| = 3, (b) |z| = 3, (c) |z| = 7. I z2 + 3z – 10

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

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Q: Q5 Find the area of the portion of the surface inside the sphere 2x = y² + 2² x² + y² +2²=4.

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Q: Which of the following is the total length of the curve of intersection of the surfaces x2 + y? + 22…

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Q: f(x) = √√/x = -²x³12 about the x-axis for 1 ≤ x ≤ 3. .3/2

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Q: Explained every step

A: The given equation of the surface is  x2 + 2y2 + z2 − 4x + 4y − 2z + 3 = 0.   The general equation…

Q: Let C be the upper half (yzo) of the circle x² + y2 = 16 from (4,0) to (-40). √ (ax 2-3y) ds =

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Q: 口 3. Which equation represents a circle with center (-5, 8) and diameter of 14?

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Q: GYa Ph the Circles 2. X+ y?8 44 Y416=0

A: 1. x2+y2+4x-4y+4=0 The standard form of the equation of a circle is, x-h2+y-k2=r2 ......1 Convert…

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A: Given; x4-3x+7=y3 on the interval [3,5]

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A: Changing the variables

Q: 1 Set up and evaluate , 6x dA, where R is the rectangular region with corners (-2, 0), (3,0), (-2,…

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Q: Draw the bifurcation diagram for à = (x + 1)(x² – 2.x +r).

A: We are given : Now, the bifurcation diagram for this is :

Q: e2z dz, I (z+ 1)* (b) Where C is a circle |z| = 3

A: The given integration is ∮ce2zz+14dz where c is the circle z=3 Here the pole z=-1,which is of order…

Q: The center of D, is (Ro, R270}

A: THIS IS FALSE.

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Q: Identify and sketch the surface by plotting different traces of (x – 1)2 – (x + 2)2 - (z + 4)² = 0.

A: According to the given information, it is required to identify and sketch the surface.

Q: ƒ(x) = √√x - 12/1x²³/2 about the x-axis for 1 ≤ x ≤ 3. 3

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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: 3. (a) Find the coordinates of the points: A, B and C in the figure. A (b) Find the areas of 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: ort er 2x² + 2y² + 4x + 8y + 8 = 0 is the equation of a circle with center (h, k) and radius r for:…

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Q: (a) (₁, ₂) (b) (r1,73) (c) (r2,73) r₁= [3 -1 0], (d) r1 xr2 (e) ri Xr3 (f) r₂ × 3 r₂ = [-2 0 1], T3…

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Q: Find the minimum distance from the point to the surface z = V7 - 2x – 2y. (Hint: To simplify the…

A: We need to find the minimum distance from the point A (-2,-2,0) to the surface z = 7-2x-2y…

Q: Use cross products to find the area of the quadrilateral in the xy-plane defined by (0, 0), (1, -1),…

A: The quadrilateral is formed by the vertices in the xy-plane defined by 0, 0, 1,-1, 3, 1, and 2, 8.…

Q: Given that Z = 6x4y+3x³y2 find Zx at the point (2,6)

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