(4– x² – y²) dA Evaluate the double integral JI 2M+3N+2P d) where coefficients M ,N,P are the last three digits of your index number and C is a positively oriented region bounded by the semi circles with radii r, =1, r, = 2 centered at the origin and lying in the first and second quadrants of the Cartesian plane.

Q: 3.1 Use the Cauchy integral formulas to evaluate the eiz cos z -dz, Ie z2(2z – 37) | where C is the…

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Q: 3.1 Use the Cauchy integral formulas to evaluate the eiz cos z *zp- Se z?(2z – 37) where C is the…

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Q: The following problem is similar in spirit to some which were studied by Archimedes and others.…

A: Let Ah be the closed region in the coordinate plane defined by the vertical lines 1 = x and x = h…

Q: 1. The solid in the first octant bounded by the coordinate planes and the surface z = 1- y – x2.

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Q: |Use Green's Theorem to evaluate [(3x² +y)dx+4xydy where C is the triangular C region with vertices…

A: The solution is given as

Q: 3.1 Use the Cauchy integral formulas to evaluate the eiz cos z -dz, La 22(2z – 37) where C is the…

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Q: 6. (The fractional residue theorem) Show that sin(ar) L r(r² + 1) tz = 5(1 – e~“), a>0. iaz [Hint:…

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Q: с 2 0 Use Green's theorem to evaluate the line integral _cos fc (2tan x − 2y³) dx + (ä⁰⁹ y + 2x…

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Q: 3.1 Use the Cauchy integral formulas to evaluate the eiz cos z dz, L.7(2z – 37) where C is the…

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Q: The area of the surface formed by revolving the graph of x = /ỹ on [2,9] about the x-axis is given…

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Q: 3.1 Use the Cauchy integral formulas to evaluate the eiz cos z dz, Le 2(2z – 37) where C is the…

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

Q: Find the value(s) of c such that the area of the region 2 bounded by the parabolae y = x² – c² and y…

A: see below the answer

Q: dr Consider the integral I- composite Trapezoidal rule with n-4 subintervals is: The approximation…

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Q: 5. Find the volume of liquid needed to fill a sphere of radius R to height h (Figure 18). R h…

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Q: 1. Find the area of the surface the part of the plane 3x + 2y + z = 6 that lies on the first octant

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Q: The region between the curve y = Vxe- and the x-axis for0 <r<∞ is rotated about the r-axis to create…

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Q: 2. Let R be the region inside the curve C :r=1+ cos 0 and to the right of the line l :r = 3 sec 0.…

A: To find point of intersection equate both r and find value of  θ which lie in the interval -π,π For…

Q: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &amp;3, x2-y2=3 &amp;4 Where u=xy and v=x2-y2

Q: Use the Cauchy integral formulas to evaluate the  ∮c eizcos z/ z2(2z -3π) dz,  where C is the region…

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Q: D Use cylinedrical coordinates to calca late the integral f fex,y,2)=2 above thedisk *ry?s4 in and…

A: given  disk x2+y2≤4 surface z=16+x2+y2 to find  to calculate the integral of fx,y,z=z over the…

Q: Consider the contour integral P. (-2 + 4)² 1 dz where C is the closed contour consisting of the real…

A: In this question, we evaluate the complex integral by using the Cauchy residue theorem. given that…

Q: Which of the following equals to the area of the plane region bounded by the ellipse 4x²+y² = 4.…

A: Option 1 is true.

Q: 17. Evaluate the integral: S, 9x? – 6dx. 18.Determine the center of the circle x² +y² = 25. %3D

A: (17)  Given that I=∫-159x2-6 dx It is known that ∫xndx=xn+1n+1 So, I=9x33-6x-15 =3x3-6x-15 Now we…

Q: Suppose f(x, y, z) = x² + y² + z? and W is the solid cylinder with height 9 and base radius 5 that…

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Q: - Prove that the contour integral – z)dz = -12i where C is the triangle with points 0, 3i and -4…

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Q: 1. Use a parametrization to express the area of the given surface as a double integral and then…

A: Here we will cylindrical co ordinate system to parametrize the surface  x=r cosθ , y = r sinθ , z=z

Q: to find 2y dx-xdy, Use where C is the green's theorem the the eircle wi'th radivs 4 Centered at…

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Q: Compute the area of the region in the ry-plane wich is bounded by the z-axis and the curve r(t) = (t…

A: We need to calculate the area bounded by the curve: r(t)=t-sint, t21-t and the x axis in the domain:…

Q: 15 tind the voleime of the solid senerated by revoling the following region about the y-axis, The…

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Q: 3. By using Green's Theorem in the plane, evaluate | (y - sinx) dx + cos x dy where C is the…

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Q: Consider the plane region bounded by the graphs of y = k, y = 0, x = 0, and x = b, where k &gt; 0…

A: Given: The plane region is bounded by the graphs given as follows, The plane is drawn for the given…

Q: Let w be an exact one-form on R², and suppose that its integral along the line segment from (0, 0)…

A: Given: Let's assume that w is an exact one-form on ℝ2 with an integral equal to 4 along the line…

Q: 3. Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x - 2y + 3 = 0 and y…

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Q: Q7. Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary o the semi annular…

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Q: Find the exact area of the surface. :=+2y,0sxS1,0sys2 Oa 2+ n(4) Ob. Sin(3) 4. Oc3-In(5) Od 5…

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Q: Consider the surface: S:z = 4 – a?, in the first octant and bounded by x² +y°, as shown in the…

A: The equation of the surface given is as follows: z=4-x2 The surface is bounded by the curve x2+y2=4.…

Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: Line integrals

Q: 4. Let C be the positively oriented circle centered at the origin with radius r> 3. Without…

A: Given: Let C be a positive oriented circle centered at the origin with radius r&gt;3. Without…

Q: Find the area of the part of the plane defined by 3z + 2y + z 12 that lies in the first octant.

A: Given equation of plane :  3x+2y+z= 12

Q: An integral expression for the area of the surface generated by rotating the line segment joining…

A: Given that: Points are- (3,1) , (6, 2)

Q: 17. Let R be the region between the graphs of y = 1 + e* and y = 1-e* on [0, In 2]. Find the center…

A: Here, f(x)= 1+ex g(x)=1-e-x a=0 and b=ln2

Q: Consider the 2nd order PDE -3u +6xu-3u w=cos(x). XX ху yy (a Determine the regions in the xy-plane…

A: Consider the PDE: -3uxx+6xuxy-3uyy=cosx. A second order PDE of the form…

Q: Let D be the solid region in the first octant bonded above by z-3 and below by 2= 2++y. Then the…

A: Here we will have to project the 3-dimensional solid regions on a 2-dimensional plane. Hence, we…

Q: Evaluate || 4.nds , where A=zi+xj – 3y°zk and S is the surface of the cylinder x² + y =4 included in…

A: Let ∅=x2+y2-4  Then the normal to the surface S is ∇∅=2xi+2yj The unit normal is…

Q: 1. Use a parametrization to express the area of the given surface as a double integral and then…

A:

Q: Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant. (Use…

A: Part of the plane equation   5x+4y+z=20⇒z=20-5x-4yPlane lies in the first octant , so x≥0 ,…

Q: 2) Use a change of variables to evaluate , zdV; where Dis bounded by the paraboloid z = 16 – x - 4y?…

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Q: Find the area of the part of the plane  5x + 3y + z = 15  that lies in the first octant.

A: From the given statement, the plane is 5x + 3y + z = 15 and it is lies in the first octant.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.