1. Determine the limits of the sequences (an), (bn),(Cn) and (dn), where 6n2 – 7n An b, = Vn² + 6n – n , 2n2 +9 8n+1 + (-6)" Cn = 2n+2 + 8" + 6' n+1 ( 2n + 1 dn + Vn² · 6n+1. 2n

Q: X4 X6 x8 x10 3. Y = x2 + 3! N Terms ** * ... 5! 16 1L +

A: Please rate and feel free to ask any query

Q: (1) IF: ā=21-j+ k, b=i+2j- 3k, č=-3i+2j+ k Find : a.b, ã.č, č.ã‚ (a+b).(a−b),(ã+ê).(ā-č) (a +2b-3c).…

A:

Q: zn 3n+1 7. 4-2n nニ」

A:

Q: Show that P(n, 1) + P(n, 2) = (22) – 2 (2), for integers n ≥ 2.

A:

Q: 6. Prove that x² dx b³ - a³ 3 3

A:

Q: 2. (s² +5

A: The given function is -tcos5t To find the Laplace transform of the given function proceed as follows…

Q: 5. (x²-x)? 5.*- 5. - x2 – 2x + In|x|+C x3 2 6. S(6Vx – x-3)2 dx 6. 18x? + x3/2 8 1 + C 5x5

A:

Q: 9) (5y + 8y) - (4y + 3y') 10) (2x' + 6x) + (3x - 4x)

A:

Q: 7. (D² + D²)z = a²y²

A:

Q: 3-J (х* + 2х 3) dх

A:

Q: Q2. P(A) = 0.42, P(B|A) = 0.66 and P(B|A’) = 0.25. Find the following – P(A’), P(B’|A), P(B’|A’),…

A: We have given information, P(A)=0.42 PB|A=0.66 P(B|A')=0.25

Q: dz IV100-49(In z)?

A:

Q: Given g(x) = 6x – 15x +4x +8x–4 and )= 3x² – 3x – 1, what is the quotient ? A 2x – 17x+10 A 2x-5 B.…

A:

Q: Find a formula for +(−1)n. (2). 1 1 ¹ – ²2 ( ² ) + ² ( 2 ) - -· ··- 1 n+1

A: To Find: A formula for .

Q: 6. (t -1)+(2 8. (2x² +5xy+ 3y²)+(8x² –7y²)

A: 6.

Q: L{5cosh2t-3sinht} 1. 5s 3 a. s²-4 s²-1 3 5s b. s²+4 s²-1 3 5s C. s²-4 s²+1 5s 3 d. s²-4 s²-1 - +

A:

Q: (6) s(4) + 4s(³) + 5s(²) + 4s' + 4s = 0.

A: (.) Given differential equation is,     We find the solution by the method of differential operator.…

Q: has its largest value. a = Find two numbers a and b with a ≤ b such that b= # # L (6-52 (6-5x-x²)…

A: Given integral is ∫ab6−5x−x213dx. We have to find the value of a and b with a≤b. The integral…

Q: Using chain rule, what is the (2x-¹-3x)³ ? da O 24+108x²+54xª+81x6 x4 -24+36x²+54x4 -81x6 x4 O…

A: The objective of the question is find the derivative .

Q: dx 11 J V64x2 - 121 8 11 18 – In-x+ 8 3 A +C 64x2 – 121 B In 1 V64x2 - 121 +C 11 In V64x2 - 121 +C…

A:

Q: dx 16. S 9x2-4 |3x+2 A. In +c B. In D. tn +C + C + C |3x+2 |3x+2| 3x-2

A: This is basic integration problem

Q: 20 %3D Find (all) the value(s) of c such that 5c2n 3 n=0 (A) c= 2 (B) с — 7 (C) c= -2,2 (D) c = |…

A:

Q: 4 4 + x2 Find 3 x° + + 4/x ) dx - -

A: Given integral, ∫x3+4x+4x2+4xdx

Q: 3 - 4 fX = the value of X" is - 1 %3D

A: We have to find the value of X^n

Q: By using the substitution u = 4x + 1, evaluate (4х + 1) dx +x + k 4x? + x + k (4x + 1)² + k x' + x +…

A:

Q: 6. b = 1+35 + 35, 5 +3 A, 5+3-1= B a. If (25)* = (125) then determine y: x b. Show that, b³-3b-6b-4=…

A: Note:- For this problem, you don't mention about "b" in part (b), Will i have to use values of b and…

Q: -2x xp- (1-x)' 7. Evaluate A. +6x-n(1-x)+-(1-x)* +C C. '+6x + n(1-x)' + (1-x)*+c D. x+6x + In(1-x)"…

A:

Q: 1/2 z + 6 = 3/2 (z + 6)

A: We have to solve for the value of z in the above equation.

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.