Solve the recurrence relation subject to the initial conditions. T(1) = -1 T(2) = 7 T(n) = -4T(n-1) - 3T(n-2) for n ≥ 3

Q: 2. (a) Calculate (i+1)302 + (i − 1)302 and write it in the form of x + iy. (b) Find an upper and…

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Q: (1+x(2)- 2x(2)(1 + x)(2x) (1 +x)*

A: Apply BODMAS rule, to simplify the given expression. First, remove the parenthesis and then…

Q: Let f (x) = 2x +2 and g (x) = –3x+1 Find g(f(2)) O -17 O -18 O -35 O 18

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Q: For x = (-∞, ∞), determine the rank r(A), where -3 -3 2 -1 5 x 4 x + 5 1 x + 3 1 1 A = 1 -1 0 0 -2 x

A: Given that .We need to find .

Q: B = {1 + x + x, x + x2, x2}. for P2. Let p(x) = 2+x + 2x?. Then [p(x)]3 : %3D %3D 2 - 1

A: Using linear combination of three polynomials

Q: (a) I multiply a third of a quantity plus a unit by a fourth of the quantity plus a unit, and it…

A: (a) Let the unknown quantity be x. One third of the quantity is x/3 and added by one unit gives…

Q: 2 3 0 1 B:= |1 2 1 1 2 1-1 0 := |1 0 1 1 0 0 0 0 1101 Q2. Let (a) Determine if x is in row(B). (b)…

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Q: (8) A company produces X bulbs per day. If E(X)= 1000 and var (X) = 100, then P(900 < X < 1100) is…

A: Given information: EX=1000VarX=1000 Chebyshev's inequality: PX-EX≤a≥VXa2

Q: Using P3(x) =[5x³ – 3x] and P4(x) =[35x* – 30x? +3], generate the next Legendre polynomial using…

A: It is known that the Legendre polynomial satisfies the following recurrence relation.…

Q: B = {1 + x+ x', x+x?, x). %3D for P2. Let P(x) = 2 + 3x + 2x. Then [P(x)]s = %3D None

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Q: F L (a) Given A = use the Cayley-Hamilton theorem to find (1) A¹-3A6 + A¹+ 3A³ - 2A² +31 (ii) A*,…

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Q: Graph the function. for -4 <x<-2 for -2 sx<3 5) m(x) = {x V -3 for x23 -10 4 4

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Q: 1 Given f(x) =1¹2, determine the sum of 4-x² n 16h +00 by differentiating f(x). n=1

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Q: 2n [3] (b) E for n 21 2k k=0

A: Answer

Q: P (X=(X+X/3 ), for x = 0,1,2 3 4 find what's to come P(x 2 3) P[( x=3) U(x=4)]• P(x=3) + P (x=4)•

A: Given P(X) = 1D(X + X/3)  ,  for  x = 0, 1, 2, 3, 4

Q: K2. A dividend of P(x) = 6x² + 2x³ + 3x² - 11x - 9 gives a quotient of Q(x) 2x³ + x - 4 with a…

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Q: Find the value of c if ∞ (1 + c)−n   n = 2 = 1

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Q: If [x² - 2x + a] = 0 has no solution, then find the values of a (where [] represents the greatest…

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Q: (7) Let X P(a) and E(x)= E(5-5x), then 2 is. (a) 25/26 (b) 26/25 (c) 12/26 (d) 26 (e) None of these

A: We know that the if X~P(λ), then E(X) =λ

Q: (2x +1 f(x): 1-2x+3 if x21 if x<1 10 8- 10-8-64-2 68 10 하 2.

A: We have to draw the graoh of given piecewise function. Please see the conclusion below.

Q: f(0.5) = 0 and f( -1) = 6 indicates that: * O There is no remainder when f(x) is divided by 2x - 1 O…

A: Answer is first option.

Q: If [x² - 2x + a] = 0 has no solution, then find the values of a

A: We have x2-2x+a=0⇒x2-2x+a∈[0, 1) Given that equation has no solution ⇒x2-2x+a∉[0, 1)

Q: Use initial value theorem and final value theorem to find f(0) and f(), if 6+7s2 + 5s F(s) s(s? + 4s…

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Q: Given that Z- N(0, 1), find the value of m, given that: (a) P(m <2< 2.878) = 0.4968 (b) P(-0.674 < Z…

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Q: Let f(x) = (x – 1)2 + (x + 1)³. Find the sum. f(1) + f(2) + f(3) + f(4).

A: Givenf(x)=x-12+x+13

Q: (7) Let X × P(1) and E(-x)=E(5– 5x), then 2 is. (a) 25/26 (b) 26/25 (c) 12/26 (d) 26 (e) None of…

A: Provided information is ; X ~ P(λ) we know that ; Mean of Poisson distribution is given by ; E(X) =…

Q: 1 Expand f(z) : in the domain %3D (z-6) (z-9) 6 < [z] < 9.

A: Laurent series exaption in annulus

Q: 3(n + 1) n° + 1 lim 1; inconclusive 3n (n + 1)³ + 1

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Q: If f(x) = 3x-2 and g(x)=x+1, then (f(g))-¹(a) equals 01-2 O (3-1) O x-1

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Q: (e) [ The Method of Iteration ] Perform seven iterations to find a real root of the equations y² –…

A: Given the function fx=y2-5y+4=0 and 3yx2-10x+7=0 and initial guesses =1,2 Now, f1=y2-5y+4=0........i…

Q: p(n) is the number of ways to perfectly cover a 2 x n grid with tiles (a tile is a 1x2 rectangle).…

A: Part(a): For 2×1 grid, 1 tile 1 way then, p1=1 For 2×2 grid, first method put the first tile in…