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

A: Answer

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: (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: 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: 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…