Let, a1 = 1, a2 = 2, b1 = 0, b2 = 1, for n > 3, 2an-1+ bn-1 for n 22 bn = bn-1+ an-1 an express an in terms of n.

Q: 2 and B= 1 0. then Show that if A = 6. -1 2 (A + B)(A + B) # A² + 2AB + B?

A: Given that A=-1201 and B=10-12 We have to show that A+BA+B≠A2+2AB+B2

Q: Find T(v) by using the standard matrix and the matrix relative to B and B'. T: R² R², T(x, y) = (2y,…

A:

Q: verify that3(AB) = (3A)B = A(3B)

A: Given matrix

Q: When multiplied out, what are the first 4 terms of (x + 3y)0?

A:

Q: 1 - 12

A: Given               2+j34-j2=

Q: s+1 s² + 4s + 13, (t).

A: Inverse Laplace transform

Q: Evaluate lim,→1 ( 고-교) 2 x-1 x² –1.

A: Given that,limx→ 11x-1-2x2-1

Q: Evaluate 10s? – 5 - L-1 2 (s² + 1)(s² + 3)²

A:

Q: (22) Let A = (-∞, -2] and B = (102, ∞).

A: Given A=(-∞, -2] , B=(102, ∞). Now, the union of two sets consists all those elements that belong to…

Q: Find the product of the real numbers  7/19*12/331*(-38/7)=

A: First we multiply the numerators and the denominators straight away, then we reduce the fraction.…

Q: find (2n +1)! = 120

A: Here we have to find the value of n.  2n+1!=120

Q: Evaluate ak+2 if ap

A:

Q: Expand (* + 2)x-2)- (x-2) O a x - 4 O b x -x- 6 x - 2x - 4x+ 8 x -x- 2 x - x O c e

A: The given function is x+2x-2-x-2.

Q: 5. (CLO3) Prove that (n+3) = ("+²) + (+¹) + () for every positive integer n.

A: We need to prove        n+3C2 = n+2C2 + n+1C1 + nC0    We know, for any positive integer n and k…

Q: L4 for x2+1 고 on [-2,2]

A:

Q: Express the following in the form a + ib (for real a and b): 1 (a) 6+2i (b) (-+ i)¹ (c) i², i³, i4,…

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Q: Find the x3 term in (x-1) (2x-2)4   4=n, 5 terms

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Q: Find 1- fext=/4+|3*

A: To solve this question we need have some standard formulas of differentiation

Q: What is the product of -1+ x* and x2k + xk + 1?

A: In this question, we have to solve the expression using exponent concept. Exponent and Power The…

Q: 8 105 = 8 8 8+102 +. + %3D (1+r)' (1+r)² (1+r)³ ' (1+r)*

A:

Q: Vector A = 6i + 2j - 3k Find the

A: Given: Vector A=6i+2j-3k  To find: Scalar component of A perpendicular to the x-axis.

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 1.2 Is y = r² a solution of xy" - 2y = 0? Justify your answer.

A: Given differential equation is We have to check whether  is the solution of the given differential…

Q: Show that dx =に 3+ Vx x3/2 – 3x + 18VX- 54 In (3 + V) +C

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Q: Еxercise 13 Determine how тany times 0 арpears in thе тultiplicatioп table for Z16-

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Q: Compute: [2 1 0 5 - ] [ ] -5 ܗ

A:

Q: Find x so that x,x+2 and (x+3) are threee consecutive terms of GP

A: When a, b, c are in gp then b^2=ac.

Q: If 8 = (AB) - (AB)o, then with usual notations, prove that [(A) – (a)][(B) – (B)] + 2N8 = (AB)?+…

A: Given:-                A-αB-β+2Nδ = AB2+αβ2-Aβ2-αB2

Q: S3 ¹(s²-2s+2)(s²+2s+2)· e. L-11 7

A: In this question, we need to find the inverse Laplace of the given function.

Q: For a, b E R, calculate (ax + b)dx (x²+1)²(x²+4)*

A:

Q: Find x so that x,x+2 and (x+3) are threee consecutive terms of GP

A:

Q: 7over9 + 3over4 - 2over3 =

A: We have to find the value of ,      7 over 9 +3 over 4-2 over 3

Q: S + (2 + ² + 2)²³² de 호 t

A: Given, ∫t2t2+2-12dt

Q: X=6{2+3[2(8-3)+(4+1)-2]}

A: Given,          x=62+328-3+4+1-2

Q: Given y=63x+1, find y". A 3x(3x+1)63x-1 B (9)63*+1 © 63x+1 D (3in6)263*+1

A: Given, y =63x+1 then y'' = ?