5. Let C denote the positively oriented circle z- 1= 3. Evaluate the integral: 3 z +2z dz 3. (z- 2)

Q: A circle has its center at (3,-2) is tangent to the line 3x+4y-26=0. Compute the point of tangency…

A:

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

A: Given that:∫C8-zz(4-z)dz, C is a circle of radius 7, centre 0, negtively oriented.

Q: 6. For any closed surface S, prove that || CurlF.N dS=0.

A:

Q: Compute the line integral (Баллов: 2) Jo ds, Cis the right half of circle x2 + y 16 (counter…

A:

Q: Let C be the positively oriented circle x? + y? = 1. Use Green's Theorem to evaluate the line…

A: Compare the integral ∫C19ydx+20xdy with ∫CMdx+Ndy to obtain M=19yN=20x Consider…

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

A: C : circle with radius 7 and centre 0, negatively oriented  f(z) = (8-z)/(z(4-z)) Singularity of…

Q: 10. Evaluate , (2x – y) dA where D is bounded by the circle with center the origin and radius 2.

A:

Q: 10. Let C denote the positively oriented circle z| = 1. Show that - Ti 2sin(z) dz cos(z) dz 4 z(z²…

A: See the attachment.

Q: By using polar coordinate, evaluate Sl, x² + y² dA, if R is the region in between circle x² + y² = 1…

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Q: Evaluate the line integral xdy- xydx over the closed path C where Cis the circle C

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Q: Calculate the line integral ∫Cy2ds, where C is a part of the circle x=acost, y=asint, 0≤t≤π/2.

A:

Q: 7. Use Green's Theorem to evaluate the integral f x²y dx - xy²dy where C: is the circle x² + y² = 4…

A:

Q: Suppose surface #1 is defined by o =45° , 0 <ps9, 0 < z< 6 and surface #2 is defined by 0 =56.3° The…

A: given:

Q: Let C denote the circle of radius 1 in R2 centered at the origin, oriented counterclockwise. for…

A:

Q: Let r < R. Revolving a circle of radius r, (x – R)² + y² = r², around the y-axis gives a donut…

A:

Q: In which of the following cases the circle T NS has radius R = 2 and center C = (1,-1,0)? %3D O (a)…

A: To solve the following problem

Q: Find the area of the inner loop of the curve r= 1-2cos θ

A: For the inner loop of the curve 1-2cos θ=0⇒2cos θ=1⇒cos θ=12⇒θ=cos-112⇒θ=π3,5π3

Q: The intersection between the surface x + y + z = - 1 and the circle x2 + y2 = 1,z = 0 is

A:

Q: 2.2 Find upper bound of z + 4 -dz (z – 3i)3 + 1 where C is the circle |z – 3i| = 4.

A:

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

A:

Q: Use Green's Theorem to evaluate the integral (2x? – y)dx + 4xdy where C is the circle x? + y² = 9…

A: To evaluate the given integral using green's Theorem.

Q: Let C be the circle |2- i 2 oriented counterclockwise. Evaluate the following integral 1. z(2² + 4)

A:

Q: 23 + 3 4. Evaluate the integral dz, where C is the circle (a) |z + 3| = 3, (b) |z| = 3, (c) |z| = 7.…

A:

Q: # 4. Evaluate the line integral | (x +2x²y) ds, where C is the upper half of the unit circle x2 + y2…

A:

Q: 6. Compute the contour integral (a) / COS Z -dz where C is the positively oriented circle |z – 1| =…

A:

Q: 8. Let Ci denote the positively oriented boundary of the square whose sides lie along the lines x =…

A:

Q: -) Let -y M(x, y) = x2 and N(x, y) = + y? x2 + y? how that ƏN ƏM dx ду ) Show that -y F(x, y) = x² +…

A: Given :-  A vector field for conservative field in the plane ,  ∂N∂x = ∂M∂y To Determine :-  M x,y =…

Q: Find the integral fc ez dz where C is the circle |z| = 3 in CCD. (z – 1)2(z – 2) %3D -

A:

Q: Determine the osculating circle of the helix defined by y = x^3 − 3x + 1 at x = 1.

A:

Q: Let C denote the positively oriented boundary of the square whose sides lie along the lines x =+ 2…

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: Jse Green's theorem to evaluate $ (2°e* + 4y) dz + (-5x+ y* sin(y)) dy, where C is the…

A: The given path C is circle x2+y2=16. Therefore: D= (x, y) : x2+y2≤16

Q: 3. Evaluate the integral *zp- where C is the circle |2| = 2.

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: Let C consist of the part of the circle r +y = 4 from (2,0) to (0,2), Followed by the line segments…

A:

Q: By using Cauchy's integral formulas evaluate sin Tz2 + cos TZ² dz (z + 1)(z – 2) C and e2z dz (z –…

A:

Q: Express the circle specified by a = 2 cos(0) y = 1+2 sin(0) in Cartesian coordinates and find the…

A:

Q: Evaluate [[[ =*dxcydz over the sphere x +y² +=² =1.

A: to find:- to evaluate the given integral.

Q: Let C be a curve given by the intersection of the surfaces z = x2 +y2;z = 3−2x . The value of the…

A:

Q: Find the centroid of the arc of the circle r = 2sin0 + 4cos0 from 0 = 0 to 0 = T1/ %3D O (2.637,…

A:

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: Given that o is the part of the surface z = 4 – x in

A: Given, the surface z = 4 - x in the first octant from y = 0  to  y = 2. If ψx, y, z=xyz, F(x, y, z)…

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

A: In this question we have to find the Integration.

Q: Express you answer in Mdx + Ndy = 0. 1. Circles whose center is passing through y = 4x %3D

A:

Q: Let F = -2yi + 2xj. Use the flux form of Green's Theorem to compute F·n ds where C is the positively…

A:

Q: Let YR be the arc of the circle {|z| = R} that lies between the ray Arg(2) = T/4 and Arg(z) = 37/4.…

A:

Q: Evaluate the line integral ∫Cx2yds along the segment of the line y=x from the origin up to the point…

A:

Q: Calculate the double integral ∬R(x2+y2)dxdy in the circle x2+y2=2x.

A: Write the equation of circle into standard form. The radius of the circle is 1.

Q: Let YR be the circle of radius R with counter clockwise orientation. Prove that 1 -dz = 0. lim z3 +…

A:

Q: 7. Find the area of the portion of the plane z = 2 y that lies directly above the circle x+(y-1) =1…

A:

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

A:

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.