b) Let C be the circle |z| = 4 traversed once in the positive sense e~2 (counter clockwise). Compute : f. dz z² (z-5)

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

A:

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

A:

Q: 4. Compute, ydx + xdy x² + y² where C is the circle centered at the origin of radius 2 oriented…

A:

Q: 5. Let C be the circle x +y} =4_which is positively oriented. Let C, be the upper half-circle C1 =…

A:

Q: Let YR be the circle of radius R with counter clockwise orientation. Prove that 2 – 1 - lim R00 YR…

A:

Q: e? – 1 (b) ( - 1y2 dz where C is the positively oriented circle |2| = 3. %3D z(z – 1)2

A:

Q: Find the curvature k of the circle C : (x – 2)² + (y + 3)² - at the point (5, 1).

A:

Q: Use Green's Theorem to find SF ·dř where F = (y³, –x³) and C is the circle x² + y² = 3. %3D %3D

A: The given vector is  F = y3i - x3j

Q: Use the Trapezoidal Rule with n=6 to approximate π∫0sin2xdx.

A:

Q: Q2 Calculate 8- z dz, z(4- z) where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: Use Green'sTheorem to evaluate O ydx – xdy where C is the circle with center at the origin and…

A:

Q: Q2 Calculate 8- z dz, z(4-z)* where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: Set up and simplify (but do not evaluate) : 3x ds, where C is the arc of the circle r2 + y² = 4 from…

A:

Q: For what minimum integer value of a, will the line ax+(a+1) y =18 www (a> 0) have two intersection…

A: If the line cuts the circle at two points then given line is secant line of the circle .The…

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: What is the ALGEBRAIC RULE for REFLECTION over the line y = x? (х, у) —

A: This question is related to reflection of coordinates, We will solve it using given information.

Q: Q2 Calculate 8 - z dz, (4- | where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: Evaluate F dī , where F(x, y) = (e* +x² )î +(e' – xy²)ĵ and C is the circle x² + y2 = 25, oriented…

A:

Q: 2: Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x–2)²+(y-3)² = 4 | a) Using Green's Theorem

A:

Q: Show that the minimum distance from the origin to a point on theplane ax + by + cz = d is

A: Given: ax+by+cz=d we know that minimum distance p of a point x1,y1,z1 from given equation of plane…

Q: =2) Calculate & ydx + xz² dy - zy³ dz, where c is the circle x² + y² = 4, Z=3 (conterclockwise)…

A: We will use stokes theorem to find integral

Q: O Evaluate + z )ds where C is the circle F(E) = for 0EEE Zo

A:

Q: Please evaluate (3y – einl2) dr + (7x + V yt + 1) dy, where C is the circle x² + y² = 9. Hint: use…

A:

Q: Q5. Prove that the circle {(x, y), x² + y² = 1} is not homeomorphic to the interval [-1, 1].

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: Ue langrange multipliars to fined the Shortest distancé fam the to the pGine x+g+Z=1. point (7,0,)

A:

Q: Find the length of the curve. 2,3/2,0 st s9 x= 4t, y 3 61 242 2 3 O 2. seçenek 4. seçenek 122 61 3 3…

A: We can find the arc length as below

Q: zt e dz if t>0 and C is the circle z]=2. Evaluate 2ni C 2πίz+1

A:

Q: Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x-2)²+(y-3)² = 4 Without using Green's Theorem.

A: We will find out the required value.

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: 6. In the accompanying diagram, PQ is tangent to circle O at Q and PRT is a secant. If mZP - 56 and…

A: To find : m arc QR

Q: Evaluate P (3x + 4y) dx + (2x – 3y) dy where 'C is the circle x?+y = 4.

A:

Q: 4. Let C be the the circle ² + y² = 4 and Calculate the work(W = [,F dr when C is traversed in the…

A:

Q: Let C be the line segment connecting 0 to ni. Then f. 1-e2z dz =

A: we have to find integration

Q: Exercise 1.2.16 Find the circle x2 +y² +ax+by+c=0 passing through the following points.

A:

Q: Evaluate |*(x + 7) – 2y ds where C is the circle of radius 1 centered at (-3,0) and lying on the…

A:

Q: nath A = 30, B = 20, C = 11, D = 22. 3. Discuss how to evaluate Z enclosing the origin. dz, where C…

A:

Q: Let f (z) -Let C'be the circle z 10in the counter-clockwise direction. What is 1 -Lf(2) dz? 2ri

A:

Q: Evaluate f. y3 dx - x3 dy where c is the circle x2 + y2 = 4

A:

Q: Consider the line L = {z = x + iy e C, y = 1} Let C = {w 1 -, z € L} with Convince yourself that C…

A:

Q: Evaluate f.y ds where C is the upper half of circle x? +y² = 9, traversed in the counterclockwise…

A:

Q: Use Green's Theorem to evaluate - – In(x² + y²))dx + 2 tan¬²(y/x) dy, C is the circle (x - 4)² + (y…

A:

Q: 6. Compute G.T ds if K is the portion of the circle x2 + y* = 7 in the third quadrant (oriented…

A: region of integration is part of circle, x2+y2=7, lying in 3rd quadrant, thus, limits of x,y are -7…

Q: Find the upper bound of |[∫c ez^2 + 1 / (z - 1)2 + 5] dz|, where C is the circle |z - 1| = 2.

A:

Q: 2e% Let f (2) = Let C be the circle (z – 4) (z – 6) 2 = 8 in the counter-clockwise direction. |2|

A: Solution

Q: Use Green’s theorem to evaluate the line integral 2x2y dx + 6x3 dy, where C is the circle x2+y2 = 4,…

A: The answer is as follows:

Q: dz b) C: z|= 4 is a circle calculate the integral .(z-1)(z² +9)

A:

Q: Q5. Prove that the circle {(r, y), x² + y? = 1} is not homeomorphic to the interval [-1, 1].

A: Here we can prove this question using topological property connectedness.

Q: Q2 Calculate 8- Z -dz, (4 – 2) where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: Let C be the circle |z| = 4 traversed once in the positive sense (counter %3D clockwise). Compute :…

A: