Integrate counterclockwise dz by Cauchy's formula 9. - 3 counterclockwise around the circle C : |z – 3 – 3i| = T. 2 - dz || -

Q: (x-6)²+(y+6)²=26 What is the radius of the circle?

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Q: Let f (2) = . Let C be the circle |2| = 2 in the counter-clockwise direction. What is | f (z) dz?…

A: This problem based on Cauchy's Integral formula. See the solution.

Q: Which among the circles has radius 5 units? (x- 3)2 + (y – 4) = 25 %3D (x- 3) +y-4)² = 5 (x-4) +…

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Q: P(t) denotes the point on the unit circle U that corresponds to the real number t.

A: The x-coordinate of any point on the unit circle represents cosine value and y-coordinate represents…

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…

Q: (x-15)²+(y+10)²=20 What is the radius of the circle? Question 4 (x-15)2 + (y+7)²=272 What is the…

A: *to find:- Radius of circle.

Q: Find the midpoint of these two points (4, 6) and (7, 10) Use the formulas: x = (x1 + x2)/2 %3D y (yi…

A: Consider the points, 4,6      and         7,10 The midpoints of two points is given by the formula,…

Q: How would ugraph fx):()'?

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Q: 2 1 act on C2. Find the eigenvalues and a basis for each eigenspace in C2. Let the matrix - 61 12…

A: Solution

Q: Find an equation of the povalbola in standovet form focus at F(-4,0) and divectrix ;X=-4

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Q: Find the distance between (1, 1) and (3√3) along the graph of y2=x3

A: ANSWER :

Q: Evaluate (x² - y²) dx + (x² + y²) dy, where C is the circle x² + y² = 9 oriented counterclockwise.…

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Q: (x + 3)² 64 - - (y – 5)² = 1 - Distance from the center to each focus is:

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Q: Evaluate the slope at the point (2, 0) for: y² + sin(y) = 3x² - 12

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Q: Explain the geometric meaning of r'(t).

A: Let the function is given as ,  rt=ft, gt, ht The derivative of the function is, r't=f't, g't, h't…

Q: Evaluate (x+ y)ds, where C is the top half of the circle x² + y² = 4, oriented counterclockwise.

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Q: Find the inverse of the circle x2 +y? = a?, the centre of inversion being the origin.

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

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.