3) I Consider the topology = {GCR:0 ¢ Gor G = R} on R. Is open %3D %3D interval (-1, 1) compact in (R, 7)? Explain why.

Q: 2. Generate 10 normally distributed random points in 3-D space, and join them with lines in one 3-D…

A: [X,Y] = meshgrid(0:.25:5,0:.25:5); Z = sqrt(X.^2 + Y.^2); figure(2) mesh(X,Y,Z) title('surface z =…

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Q: Evaluate the line integral [6. 6ayⓇ ds, where C is the right half of the circle x² + y² = 4.

A: To evaluate :   ∫C6xy6ds, where C is the right half of the circle x2+y2=4 Prerequisite : We can…

Q: (7) Let D be the solid above the cone z = r and below the sphere of radius 2, and let fla, 4, 7) =…

A: To convert the cartesian coordinates into cylindrical coordinates put  And the integral will be…

Q: (15) Let D be the half-disk x² + y? 0. Compute / | (a + y) dA D

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Q: The value of the triple integral 6zdV where E is the upper half E of the sphere of x² + y? + z? = 1…

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Q: nclude spaces in between 5. d te In (In y)) at y dy

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Q: 3) Prove thet the xy-plane with constant curva tue k= urve In is o circle of radious

A: We have to prove that a curve in the xy plane with constant curvature k=1r is a circle of radius r

Q: 2. Given: WX = YZ; ZWXZ = ZYZX Prove: WXYZ is a parallelogram

A: Parallelogram

Q: |Use Green's Theorem to evaluate | -x'ydx+xy°dy where C is the boundary of the C circle x + y =16…

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Q: Evaluate the line integral ∫c x3 z ds, where C is the line segment from (0,8,8) to (5,7,6).

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Q: b) Show that the implicit Trapezoidal method h Wi+1 = Wi +5 f (ti+1, Wi+1) + f(ti, w;), is…

A: The solution is given below in the next step:

Q: 7. Which surface is parameterized by ř(u, v) = (u, uv, v) for –1 < u <1 and –1< v< 1?

A: r→(u, v) = u, uv, v for -1≤u≤1 and -1≤v≤1The parametric curve is  Option C is correct.

Q: 22. Compute the contour integral (Баллов: 2) Sof (2) dz, z E C, if f (z) = and path is semicircle z…

A: Topic:- application of integration

Q: Compute where Cis the counter clockwise oriented boundary of upper-half unit disc D. 0.66666666667…

A: We need to find ,  ∮ y2dx + 3xydy , over  C ,  where C is the counter clockwise oriented boundary of…

Q: and y have density flay)=82y tor Find ECX14) and ECYIX) リフズ7679 %3D

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Q: t in 30 minute please duopoly with homogeneous goods. There ar

A: When there are only two firms in the industry, it is in their advantage to collude and set the price…

Q: The sphere x² + y² +z² = 100 has the center (0,0,0) and a radius of length 50. Select one: True…

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Q: Compute (ax + by² + cz) dS over the sphere x +y +z² = 1.

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Q: 3. Evaluate ff Vr² + y²dA, where R is the region bounded by the circles with center R (0,0) and…

A: Given integral is: ∫∫Rx2+y2dA Where R is the region bounded by the circles with center 0,0 and…

Q: Consider the region bounded by the Xxy curves J 3-2x, and y=3, %3D

A: Calculating the area of the region bounded by the curves

Q: Prove that y, + y, +2y, 56 is a valid Gomory cut for the following feasible region. X-{yeZ: 4y, +5y,…

A: We have, y2+y3+2y4≤6 X=y∈Z+4 ;X=4y1+5y2+9y3+12y4≤34X=y∈Z+4 ;X=5y2+9y3+12y4+5y2≤34X=y∈Z+4 ;…

Q: Evaluate SSS z²dV, where R is the region given R by above the plane z=O and between the spheres 2. +…

A: A scalar function is a rule that is used to associate a number, or quantity with a particular point…

Q: 4 6 Let y = 7 2 40 Compute the distance d from y to the plane in IR spanned by ui and uz d =

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Q: evaluate the arca of He reginn bounded below by and y= aboue by y=X

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Q: consider surface s with parami Glusv) = cu vo uv) Compute Pa, 7 Nas Tu, Tv o of s olso compute the…

A: Given surface is, G(u,v)=(u,v,uv)

Q: The area bounded by the curve y = In(z) and the lines z = 1 and =2 above the z -azis is %3D square…

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Q: 3. Find the orthogonal trayectories to the cuve y = ax²- acx Is held fixed. 3 .2 %3D where a

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Q: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

A: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

Q: need help with 9.2.5

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Q: can u help me with pullbacks and integration plz

A: Given that the integral,

Q: 8. Evaluate the double integral // ydrdy where T is the triangle with vertices (0,-1), (0,5), (4,…

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Q: Let W be the region that is cut aut from x't v<4 by the pora blae id Rs X'ty ond the plane =10.…

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Q: (1) Compute where Cis the couater dockwise oriented boundary of upper half unit disc D.

A: It is given that, ∮Cy2dx+3xydy here C is counter clockwise oriented upper half disc D.   Here,…

Q: 13 ABCD is a trapecium with ABDC. A line parallel to AC intersects AB at X at Y Prove that ar…

A: Since you have asked multiple question, As per our policy we will solve the first question for you.…

Q: Let D be the solid region in space bounded below by p = -- and above by cosp p = . Then the region D…

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Q: 13-Evaluate JJI zdV E where E lies between the spheres x2 + y? + z2 = 1and x2 + y? + z? = 4 in the…

A: The given integration is , Let, I=∫∫∫EzdV change the integral into spherical coordinates Put x=r…

Q: let A and B be matiices of Con det A) = -1 find the Valué of Cdet(z AT) - dct(-2B )) LA Pproxi mate…

A: Given:- det(A) =-1/2   ,  det(B) =2/3 To find:- [det(AT/5) -det(-2B-1)]2

Q: Ex: © Suppise that the fuowing trausfruntiun Cowneciğa the (I') and (xi) coarduate رک سهاور؟ てス4ス)…

A: Given  x¯1=ex1+x2x¯2=ex1-x2 Required Jacobian is…

Q: Find the area of on of the triangle that can drawn between the planes 3x – 6y – 2z = 15 and 2r + y -…

A: The equations of the two planes are: 3x-6y-2z=152x+y-2z=5 As, 5,0,0 satisfies the equation of plane…

Q: 8. Use Green's Theorem to evaluate px*dx+xydy where C is the triangle with vertices (0,0), (1,0),…

A: As we know from the Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA And The expression for the equation of…

Q: 3, Let R be the of: y: sinx region endlosed bu the grophs n enclosed by and 1 x70 . Groph R and…

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Q: Use Green's Theorem to evaluate S. axy dy + cxy dy, where C is a counterclockwise oriented…

A: Given : a=2, c=8 We have to use Green's Theorem to evaluate            ∫C axy dy+cxy dy where C is a…

Q: use the funda men tal Theorem of Culculus to find the under Curue of 2. y = -xFl0 x between x = 3…

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Q: THE DiffieRENITAL ECLATDOM WITH INITIAL conoirDON. dy- XSENX こ dx 3.2

A: Given query is to find the solution of the differential equation.

Q: Show that a triangle with vertices (x,Y;), (x2,y2), and (x;,y;) has area + x,y3 + X3Y, – X,Y3 – X,Y,…

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Q: Let S be the portion of the cylinder y = 1 − x2 with x≥0; y≥0, bounded by the planes z = 2, and z =…

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