Prove that there is no permutation a such that a'(12) a = (34) (15). %3D

Q: Let X Gamma(a, B). Prove that for any positive integer n > 1, E(X") = [(a +n– 1)(a+n – 2)..-a]3".

A: It is given in the question that X~Gammaα,β then we have to prove that for any positive integer n≥1.…

Q: 2. Let A = 201-18 and /= 2 1 1 2 01 Find A(A+1).

A: A=[2 1      1 2]I=[1 0      0 1]

Q: Prove that if m*( A)= 0, then m* ( A UB) = m*( B).

A:

Q: The residues of * ƒ(z) = O 4/9,-4/9 O-4/9, 4/9 O 4/7,-4/7 4z (z − 1)(z + 2)² -4/9, -4/9 O 4/9.4/9

A: The given problem is to find the residues of the given complex function at the obtained poles.

Q: If In z + In(x – 6) = In(5x), then r

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Q: In(1+ 5.x?) 2 – 3x Differentiate with respect to x.

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Q: 0.2 Differentiate In x+1, with respect to x. x²-x+1

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Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x + 1 on [-1,3]

A: Verify Rolle's theorem

Q: Let flx)=x² and! gix)-Xr4. Find (gof)は) (fog)l-5)= (gof)(-5)= こくい(6。)

A: We have to find fog(x) ,gof(x)

Q: 6. Find f'(1) if Ax) = nx

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Q: .2 -dædy In (x) ey

A:

Q: Let H = {(1), (12)(34), (13)(24), (14)(23)}. Find the left cosets of H in A4 (see Table 5.1 on page…

A: Given H = (1), (12)(34), (13)(24), (14)(23) in A4 H =4and A4 =4!2 =12 So , Number of distinct left…

Q: 2F. n 1 ;;1=2" (b), (26)

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Q: Prove that In (1tx) Lx for without using the value the orem. mean

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Q: a) Let p=13. Compute L2(3) b) Show that L2(11) = 7.

A: Here concept of field is used.

Q: Prove (1.2), (1.3), and (1.4).  

A: (a) Let x∈A∪B So, ⇔x∈A or x∈B⇔x∈B or x∈A⇔x∈B∪A So, A∪B=B∪A

Q: & 18) Vaing showj that the idently in

A: Using the identity 1+x2n=1+xn1+xn,                . . . (1) we want to show that 2nn=∑k=0nnk2.…

Q: Indicate the least integer n such that f(x) = (3æ³ + 2x²)(5æ5 + 4æ*) € O(x").

A: Finding f(x) explicitly using multiplication of polynomial. The highest power of x or degree of f…

Q: first prove that ()" <n! < ()" forn2 6.

A: We will prove                        n3n≤n!≤n3n for n≥6.

Q: 3. (a) Use the Fundamental Theorem of Calculus to determine a continuous function f: 2. x) -R that…

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Q: Prove that Σ(;) = 0.

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Q: 2 O Expand Pn = 2x +3x +) in Term of P.f,.

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Q: E Show that x'+ 3x+ 2 has 4 zerosin Ze

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Q: 5. Prove or disprove each of the following formulas or assertions: b) (A - B)' = B' – A'. %3D f) P(A…

A: Take R.H.S: B'-A' Let us assume there exists x such that,  x∈B'-A'⇒x∈B' and x∉A'⇒x∉B and…