8. Consider the set S = {(x,y) E R²: a >0 and y 2 0}. (a) Explain your answers. Find dS, S° and Ext(S), and determine whether the given subset S is open or closed.

Q: 4. Evaluate fe fds where f(r, y, z) , ) and 0 <t< 1. = 12r2 and the path C is given by r(t)

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Q: If z = e'x + y In(x), find z, and z, Zx Zy II

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Q: Let P denote the path that travels along the graph of y = x2 from (0,0) to (1,1). Let f(x,y) = √1 +…

A: Let P denote the path that travels along with the graph of y=x2 from (0, 0) to (1, 1). Let f(x,…

Q: Let X (2,3. 4) and de fined metrie on X as d(x, y) = |-y Find open ball B (2.2) = (0) O (2) 0 2.0…

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Q: Let f(x, y) = xcosy- y e*y. fry at (1,0)is equal to: -5 3 -1

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Q: b) Is there a linear map T: V → W, where dim V = 3, dim W = 4, rank T = 2, and dim ker T = 1?

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Q: The simplified DNF expression using the bellow Karnaugh map is: yz yz yz yz 1 1 1 1

A: We have to do suitable grouping.

Q: (b) A point P with coordinates (X, Y) is uniformly chosen from the unit disk D = {(x, y) : x² + y² ≤…

A: As according to the guidlines we can solve only one question please post the other question…

Q: 10. Suppose that a point (X, Y) is chosen at random from the circle S defined as follows: s= (x.…

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Q: If R is the region boundeb by the square a|+|y = 1 then ffR(y-2)dA is equal

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Q: Let M and m be the maximum and minimum values of Ax, y) = 5x + 4y on the region x +y < 49 . Then…

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Q: [2 Lo 2. and defined T: R² → R³,by T(X) = AX. Let A Find the images under T of u = |E|, and v =

A: Given a linear transformation T:R2→R3 by T(X)=AX where A= 2002

Q: 8. Let C be the perimeter of the square with vertices at the points z = z = 1+i, and z = i traversed…

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Q: The area bounded by the curve y= 3va and the lines z = 3 and T = 8 above the z- aris is square units…

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Q: Let C be the boundary of a rectangle with vertices (0, 0), (-1,0),(-1,5) and (0, 5). Then ve dx +…

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Q: | eョで)) dV=

A: Given:              ∭Dex2+y2+z232dv        d is the region in the first octant between spheres…

Q: Compute F. Oszs V1-x2 –y? Let E be the hemisphere described by and F=Vz2 + x² +y² i + Vz² + x² + y²…

A: By Gauss divergence theorem:∬∂EF·nds=∭Ediv(F)dvhere givenF=x2+y2+z2( i^+j^ +k^…

Q: . A possible initial strip (xo, Yos Zo, Po 90) for the Cauchy problem pq = 1 %3D dz p = -, q = dz…

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Q: Let ry w = and a = 2s + t, y = st, z = 2s - t dw dw Find ds' at

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Q: 6. Given: AUVW = AXYZ Prove: UV || XY .Y W

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Q: 17. Integrate f(x, y, z) = (x + y + z)/(x² + y² + z²) over the path r(t) = ti + tj + tk, 0 < a < t<…

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Q: For z + y, lim ()(1,1) Va - A. 0 В. 2 C.1 D. Does not exist.

A: This is simple question can be solve by rationalising the given function Solution is given below

Q: Use Green Theorem to evaluate $ xydx+e'dy where C is the path from (0,0) to (1,1) along the graph of…

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Q: Find the value of c such that the regionbounded by y = c sin x and the x-axis on the interval [0, ∏]…

A: Given y = csinx and the region bounded by y = c sin x and the x-axis on the interval [0, π] has area…

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

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Q: 2 let C be an arbiterery curve from l0,0) to D). (2,4) Evala vute: (3x² oy, x-2)- dio

A: To find the value of the given line integral.

Q: 2 Show that the following systems have no closed orbits in the region D x(2- x-y) y(4x – a? – 3) D =…

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Q: 2 Evaluate the fullowng cartesianntegrat changing theminte equivalent Pelarintegrals: Fー dxdy 2-

A: We have to find the double integral using polar coordinates.

Q: Let F(x, y, z) = (x-1z, y¬lz, In(xy). (a) Verify that F = V ƒ, where ƒ(x, y, z) = z In(xy). (b)…

A: Given Fx, y, z=x-1z, y-1z, lnxy (a) Verify for F=∇f where fx, y, z=z lnxy The gradient of a function…

Q: Evaluate the line integral H. dř; Ħ = e" ì + [æe" + In(z)] ĵ +2² k, and C is the path defined by 7…

A: Given H→=eyi^+xey+lnzj^+2yzk^ We know that dr→=dxi^+dyj^+dzk^…

Q: f(x, y) = xy over the triangular region with vertices (0, 0), (8, 0), and (0, 6) O 12 2 96 O 16

A: Solve

Q: Let f(x,y,z) = zIn(x³ycos(z)), find Z 3x² O In(x3ycos(z)) - ztan(z) 0 2 Y о 3z X af ila

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Q: (2) Let L be the line defined by 3 L(t) = 1 + and let p be the point (-1,6, 2). Find the minimal…

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Q: 1. Let P, X,Q denote distinct points of E. If X is between Pand Q, show that d(P,X) d(X,Q) 1-t, for…

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

Q: So lve the se cond order boundary Valye eF problem: Y+y+2yso where y (0) = || and y'lo)s 18

A: The given differential equation is y''+y'+2y=0......(1) with boundary conditions y0=11 and y'0=18…

Q: Show that the function u = p(ry) + JFÿ¢(y/x) provides the quation „Pu = 0. dy

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Q: The shaded area shown in (Figure 1) is bounded by y axis and the curve y? = (1.44 – x) m, where z is…

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Q: Let P denote the path r(t) = (7cost), where 0<t< 2n, and compute ſpF - dĩ where F = (!+ty 4 sin…

A: Let F→x,y be a vector field and r→t=xt,yt be the path of an object, where t1≤t≤t2. The line integral…

Q: Integrate h (x. y) = yi+xj over the indicated path: r(u) = ui+ u²j. ue [0, 1).

A: Given hx,y=yi+xj and ru=ui+u2j, u∈0,1 We have to integrate hx,y=yi+xj along the path ru=ui+u2j…

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 E be the hemisphere described by Oszs V1-x? -y2 and F=Vz? + x2 + y² i+Vz? + x² +v² j+Vz? + x²…

A: We can solve this by gauss divergence theorem

Q: If X and Y are two independent RVs with f (x) = e*U(x) and f „(y) = e U(y) and Z = (X – Y)U (X – Y),…

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Q: Evaluate I = Se(sin æ + 7y) dæ + (3x + y) dy for the nonclosed path ABCD in the figure. А 3 (0,0),…

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Q: If A = ze?xVi VxA at the point (2,0,3) is + 2xycosy j+ (x + 2y) k then the valueof

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

Q: 16. WXYZ is an isosceles trapezold with WX ZY If mĐW = (2x)° and mĐZ = (x +27)°, find the value of…

A: We have to find x

Q: 2. Suppose that the edge lengths r, y, and z of a closed rectangular box are changing at the…

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Q: Use Green's Theorem to evaluate x' dx + xy dy where C is the triangle with vertices (0,0), (1,4),…

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Q: 1. Evaluate | (x- y)ds over the path C:r(t) = 4ti + 3tj for 0 <t<2.

A: Answer

Q: 17. Let AXYZ be circumscribed on O R, and let XS = 5, SY = 32, and YZ = 64.* *Image not set to…

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