z²+2z-5 4.78. (a) If C is the circle |z| = R, show that lim R-00 (2²+4)(z² +2z+2) -dz = 0 (b) Use the result of (a) to deduce that if C₁ is the circle |z2| = 5, then z²+2z-5 (z²+4)(z²+2z+2) (c) Is the result in (b) true if C₁ is the circle |z+ 11 = 2? Explain. -dz = 0

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

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Q: Which point lies on the graph of the unit circle? (1,  √3) (3/4,  √7/4) (1/3,  √2/3) ( √2,  √2)

A: A point lies on the unit circle if the sum of squares of x-axis and y-axis is 1 Mathematically,

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Q: Find the limits

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Q: Find the values of a for which the point (a-1,a+1) lies in the larger segment of the circle…

A: The point a-1, a+1 lies in the larger segment of the circle x2+y2-x-y-6=0 made by the chord whose…

Q: i æ² + y? = 30 and (x + 1)? + (y – 1)² = 6 | ii (æ + 3)? + (y – 2)² = 9 and (x + 7)? + (y + 1)? = 4…

A: (i) The given circle is: x2+y2=30        ....1x+12+y-12=6       ....2

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A: (a) We have to calculate  where .in parametric form Now  and Now

Q: (4) Find the circle a(x² +y³)+b(x+y) = 1, which best fits the following data. (0, –1), (–1,0),…

A: Given that a(x2+y2)+b(x+y)=1 satisfy the given data (0,-1),(-1,0),(1,-1),(1,1)  that is it gives…

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Q: 2. Write the equation of the following circle ingeneral form and standard form. Show your work. (-4,…

A: Given query is to find the equation of the circle in stany and general form.

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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: QCA) Find the equation of the Circle whose Yadius is 3 and center C-4,-5)- (B) Find the fillwing…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: The radical axis of the given circles             x2+y2+2gx+2fy+c=0and      x2+y2+(3/2)x+4y+c=0 is…

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A: Given equation is x+52+y-12=9Write the general form of the circle

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A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

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Q: Integrate counterclockwise dz, C the circle with z2 + 16z + 63 center –7 and radius 2. dz z² + 16z +…

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A: The equation of the common chord PQ of the circles             S1:x2+y2+2x+6y=0and…

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A: given circle is                                                 we know that inverse of a function…

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A: