2.2 Prove that ne dz < 3 e 2 ++1 whore C is the arc of the circle 2| = 3 from z = 3i to z = -3. %3D

Q: -z Q2. In the circle |z| = 1, Find the upper bound for 9z4+3z²+2l

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Q: Evaluate | dz where c is the circle z| = 2. z (z+4)

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Q: 10. Use the given conditions to write an equation for the circle C (-/3, -2), a= 2 O [(x+/3) ^2 +…

A: Solution:

Q: Ex(6):-(H.W) Find the center and the radius of the circle whose eq x'+ y' +x+3y 7

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Q: ) Find an CIuation of the line tangent to the graph of Gec)=6e3X x tal dou2 o the Point (0,6). at

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Q: 4. Let C be the circle |z| = 3 traversed once in the positive sense 2z-17 (counter clockwise).…

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Q: 3. If y = 2 – 1, find the length of the graph of f from point z = 0 to a = 1.

A: Here, the given function is: y=f(x)=423x-1 To find the length of the curve from x=0 to x=1

Q: Prove that the circle {(x, y), x² + y? = 1} is not homeomorphic to the interval [-1, 1).

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Q: In circle O, tangent MN and secant MPQ are drawn to the circle from exterior point M. If MP = 6 and…

A: The secant of a circle is a line segment that cuts the circle at two points. The tangent line of a…

Q: A Point in a cadrant IV s on the init Circle. T f ts X Coordinate is 12 find the EXact value Of its…

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Q: The line tangent to the circle expressed as x² + y² = 5 at the point (x,x)= (1,2). Find the…

A: We will find out the required equation of tangent line.

Q: 3. Let C be the circle Iz| = 3, described in the positive sense. Show that if 2s2-s-2 ds (Izl # 3),…

A: Given: g(z)=∫C2s2-s-2s-zds

Q: 1 € /₁ (2² + 1)2 dz. Let C be the circle |zi| = 1. Evaluate

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Q: 4. Let C denote the circle |z – 2i| = 1, taken in the usual counterclockwise orientation. Compute by…

A: Given: Let C  denote the circle z-2i=1 z-2i=1x+iy-2i=1x+iy-2=1 So, Centre of circle will be 0,2 and…

Q: 2 b) у +3х +2у -20%3 0 2 a) x* +4у + 4х - 8у-8%3D0

A: This is a question of the Transformation of axes.

Q: dz Find an upper bound for 9c z4 –5z²+6 dz, where c is the circle |z| = 4.

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Q: e. Find points on the graph of xy°z² = 16 that are closest to the origin.

A: Let P be point (x0,y0,z0) Then, distance between P and origin is given by

Q: 2. Points L and M lie on circle K such that KL = 6x – 40 and KM = 4x– 20. Which of the following…

A: We have to find radius

Q: 7. Find a parameterization (a) line segment from -2 + i to 1-i. (b) left half of circle with radius…

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Q: 1.1 If C is circle |z – 2i| = 2, then fe + (z – 2i)*] dz = A. 0, B. 7, С. 5л, D. 10zi, E. None of…

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Q: S. r.dr = .. .?, where C is the circle x² +y² = a²,z = 0 and r = xi + yj + zk

A: The given question belonging to the vector calculus  in which we have to find the value of the…

Q: Find the area oF the loop OF the given curve. 2.y==x°C1-x)*

A: Using the double derivative in Cartesian coordinates.

Q: 9. What is the scale factor that shows ABE-CDE? C= (3, 7) B = (-1, 4) E= (0 25, 1 5) A = (-1, -1) D…

A: Use the properties of similar triangles.

Q: #3. Find 2²43 (2²4)(2+i) & с circle 121=3 dz, where C is the

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Q: 3. If y = 2 x –-1, find the length of the graph of f from point z = 0 to z = 1.

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Q: Compute . Z+1 dz, where C1 is a part of a circle with r = 3, and 0<0< %3D

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Q: Evaluate •10 (22² (x² + y²) ds, C is the top half of the circle with radius 5 centered at (0,0) and…

A: Here we will use parametric form of circle to denotes C .  a ≤ t ≤b We will use…

Q: 4. Let C be the circle |z| = 2 traversed once in the positive sense (counter clockwise). Compute: .…

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Q: The tangent to the circle x2 +y2 +10 x+5 y= 60 at the point (2 ,4) is Select one: O None O 13 y +…

A: Given that:x2+y2+10x+5y=60

Q: Find the shortest distance from the point (2,1) to the curve y = 1+√x.

A: