let f={ Ca,b) : a,bGR 3 and +,. defined on F as (a,b) + ( Cd)- (arr, bod) vla,b).(c,d) Ef Pollous: let Mon is ariny of 2x2 Ma trices and 9if-> Mare defindas fullow:- g((o.b)) = (a) rco.b).cf show that w hether. gis %3D s is e merphism or not

Q: Let y = (-4 + 35)ª. Compute O A) 6 O B) 24 O D) -6 O E) none of these

A: Calculus Question

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Q: S.モ:4-21x 84,20

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Q: KB is ∀xy F(x, y). Prove using resolution-refutation that ∀xy F(y, x).

A: Solution: First, we convert clauses to CNF : (1) ∀xy Fx,y from KB (2) ∀x Fx,Ax (3) Fx,Ax CNF

Q: Q2: Prove that: d csc-(InVx) dx -

A: The main objective is to prove ddxcsc-1lnx=-12xlnxlnx2-1. It is known that ddxcsc-1x=-1xx2-1.

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Q: the Feurier tranefrn XC10) for the Pulse f the Sapual derlribed bekw: Frind 「-2, -ろs トヒへロ X(4) %3D…

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Q: best Rank 2 approximation F ind weth respect to I|F|l the where to A -1 2 -1

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Q: * H.W Let f:AC, 9:B D be two functiens sit flx) = 96) ha fug: AUB CUp VXEANB then defred by:. %3D…

A: SOLUTION- SolutionA Rlation R:X→Y, where X and Y are setsis called functions if each element of x…

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Q: t3 dt 6) f Vt2 + a?

A: Given Data The integral is     Let,

Q: End the cquation ot the perpeadicular to tie line KEy=4tat goes thousn the point (0,2).

A: topic - equation of perpendicular line

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A: We have to find: ddxln(8-x2)3   at x = 1.

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Q: CSCX + fecy 7 CSCX secx COSX tSmx:

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Q: VXVYP(x,y) is equivalent to VyVxP(x,y). O True O False

A: ∀x ∀y Px, y is equivalent to ∀y ∀x Px, y.

Q: If w=f(p, q, r), where p-z2-y², q=y²-22, and r = 22-2², show that 1 Ow x 8x + 1 8w у ду + 18w z Əz…

A: Given w=f(p,q,r)and p=x2-y2,   q=y2-z2 and r=z2-x2

Q: 2. Let f(x, y) = (2x – y,x – 2y); (x, y) E R × R, (R is set of real numbers.) a) Show that fis one…

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Q: FP Use the Fundamental Theorem of Calculus to evaluate: /2 13. xp x zJ55 9/u5

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Q: Let f(x, y) = x for y=0 and 0 for y+0. Evaluate each of the following or if they do not exist, state…

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Q: Evaluate Se(x+ Vy). figure. d given in C3 (1, 1)

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A: Given Z~N0,1

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