Q41 state, give reasons which of the following subset are compact or not 4. {(x,y):x + yi = 1} 5- ((x, y): x + y? < 1). 6- (x, y):0 sx S 1,0 sys 1)

Q: 25.6 Let X = (Xn)nzo be a submartingale. Show that if is convex and nondecreasing on R and if y(Xn)…

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Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

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Q: 6. Evaluate (7xi - zk) · ndA over the sphere S : x² + y² + z² = 4 (u) by the Divergence Theorem, (b)…

A: The divergence theorem states that  ∬SF·ndA=∭V∇·FdV Where, F is the vector field, V is the given…

Q: 17. Evaluate the line integral xezds, where C is the line segment from (0,0,0) to (1, 2, 3).

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

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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: /Evaluate The are bounded by The Semiellipes y =2J5-x' oP The line 6 X = ±1 ,Y=-1 %3D

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Q: DATE MONTH 9- verify that l ell max alt)| defines. t elasb] %3D the Space cla,b]. morm on

A: Norm: A norm· is mapping defined on vector space V which satisfies following properties: 1. x ≥ 0,…

Q: 18. Ris the annulus in the first and second quadrants bounded by x +y² = 9 and x² + y = 36; 8(x, y)…

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Q: Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices…

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Q: - The region bounded by y = 2 -x, y = 0, x = 1, x = 2 is rotated about the x axis. 197/12

A: volume generated by revolution of the solid is 19π12 detailed solution with explanation is given…

Q: 8.F. Ifx= (1, I, --- ,)€R", define x, by e that z- l, is a norm on R'. Prove

A: Given that x=x1,x2,..,xn and x1=x1+x2+...+xn. The objective is to find the whether x1=x1+x2+...+xn…

Q: a) F(x,y, z) : planes x = 0, x = 1, y = 0, y = 1, z = 0, and z = 1. 3xi + xyj + 2xzk and E is the…

A: Solution of (a) is in given below

Q: 18) (uoe Disk Method) Find the voleime of the senerated by revoluing the region bounded bay the…

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Q: 4. If R is the total resistance of three resistors, connected in parallel, with resistances R, R,,…

A: as per our guidelines we are supposed to answer only one question. Kindly re post other question as…

Q: 1 Show that IS the separable me tre space (R, d), where el(x, y) = be-y/

A: Here we use basic real analysis

Q: (6) I. adv, where E is bounded by the planes z=0, y = 0, =0, y+= =1 and +=1, as shown in the figure…

A: Given that,

Q: Let po) - X In (x) , using the following approx im for the secoud denvative fcxo) = FOXO -h)-ZR…

A: Introduction: Apart from differentiating a function analytically, the derivative of a function can…

Q: t BLX,X) denoted set f al incod bounded operates an defined on ow hat fex every TE BLXX) for Hhe…

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Q: Solve using horizantal Slide EX Evaluat..f.x.dA.whak.R.a.the.sgen.in.the figt.…

A: ∫∫R f(x,y) dA= ∫∫R f(x,y) dxdy =∫∫R f(x,y) dydx

Q: 16. Obtain the toigonometric fouries seajes for A fit) > wt 277

A: The given image is of sine wave form. Here, period T=πand so, w0=2πT=2ππ=π

Q: Let S be the portion of the cylinder z = 1 − x2, in the first octant and between the planes y = 0…

A: We will find out the required value of a.

Q: 2 2 JEind. thePaints.an.th. sur face. Xy Z=1 that.are .... closest...t. the origin

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Q: Exercise 1 In earlier lessons, we have defined congruent to mean that there exists a sequence of…

A: To solve the congruency of  ∆ABC  and ∆A'B'C'.

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: Fimd the Valume of the Solied oblaimed by nelating the where Ris bounded by y= x* -2,X=2,X=4 and y=0…

A: I have done solution step by step in detail...just go through the solution and follow the step as I…

Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

A: Solution is given below:

Q: The solid bounded by y = 4, z = x², z = 2y, and z = 4.

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Q: Verify the Diver gence the olem for the following suffece in tegrol where à (x,y,a) = x² g*? + 2…

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Q: The scalar path integral 3(16-a y-) ds, where the path C is the straight line from the point (0,0)…

A: This is a problem of line integral. Since the path given for line integral is embedded on the x…

Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

A: The given equation of the cylinder us x2+y2=1 in the half space y≥0. Calculate the value of ∫∫∫xzdV,…

Q: the pg 2セ= Sox +3y+2= = 6 The region in the first octant bounded by the coordinate plane ytz=2, and…

A: We will find range for x,y and z and then triple integral

Q: with the p-norm 「さい Is a normed lineur s pace over fiéle cary R with respect to opera tróns addition…

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Q: 9. The solid bounded by x = 1 – y?, z = y², x = 5, and z = 9.

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Q: A natural cubic spline S on [0, 2] is given by So (x) = 1+2x- x³,0 sx<1 S(x) = s, (x) = 2+ b(x- 1)…

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

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Q: J uore program Use a soft groping of ality aith motrix copobilities to'find the eligenualves the…

A: For any matrix, A , the eigen values are calculated by solving the equation, det(A-λI)=0 . Here , I…

Q: In general, for a a) S is compact 2) Sis closed at S is compact

A: We use definition of compact metric space, totally bounded set, Closed set, accumulation point or…

Q: R Be denned by J (, 9, · Explain why we can always find the maximum and minimum of f(x, y, z) in the…

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Q: (4) In the figure, Y is compact, BEX*Y. Show that T,(B)s TB) clesed X (T, is the nýuchikn funebran)…

A: Given that Y is compact and B⊂closedX×Y. The objective is to show that, π1B⊂closedX Let's define,…

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: H-S Integrate the fallswing funCtini aver the given regionr. R: is the triangle cut from the first…

A: Evaluation of the integral

Q: (a) Suppose ƒ: [a, b] → R is integrable and L(f, P) = U(ƒ, P) for some partition P of [a, b]. What…

A: (a) Given that f:a,b→ℝ is integrable and Lf,P=Uf,P for some partition P of [a, b]. To find: what f…

Q: 4. Evaluate x²dV G where G is a solid that lies in the first octant bounded by x? + y? = 3z and z =…

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Q: 2. Find the volune og the solid gonned by revohing abaut thie lere y y=4x+1, y: -1 bounded by 4x +3,…

A: The volume for solid of revolution generated by revolving the area bounded by curves y=f(x) and…

Q: Let f(x, y, z) = x arctan z. Then solution.] af Əzəy (2,3,1)= a In 2 where a = [Show

A: Find the value of a

Q: 10. The solid bounded by y = 4, y – x = 1, z = x², and z = = 4.

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Q: Find ¹JJ²₁ z dV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,2,0), and…

A: The solid E is the tetrahedron with vertices 0, 0, 0, 3, 0,0, 0, 2,0 and 0, 0, 1. Draw the solid E:…