Use the summation notation to rewrite the following expression. (3 – 13) - (3 – 23) + (3 – 33) – (3 –- 43) + (3 – 53) – (3 - 63) + (3 – 7³) = Ý %3D k = 1

Q: 43 a. By using substitution u = Vx-1, find [ dx. x-1 b. Find [ xe“ dx

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Q: (3y+8)° (9x+1)° (X+19)° 7 ון

A: To find the values of x and y.

Q: 12x +1 S dx. (2x - 1)2 (3x + 2)2 Evaluate: (2x – 1)3 (3x +2)3 A) + C 3 8 in |(2x- 1)2 (3x+2)2| + C 1…

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Q: Expand and simplify. (8h +3) (7h² – 4h+1) - O 56h3 – 32h² + 8h + 3 - O 56h3 – 11h? 4h + 3 O 56h3 +…

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Q: 2dy Уу+16)

A: Solution of question as follows

Q: Differentiate f (x) = 71n(x²-6x+3) A. (2x – 6) 7ln(x²-6x+3) f' (x) = x2 – 6x + 3 - В. In(7) (2x – 6)…

A: Given query is to find the derivative of the expression.

Q: 4. 7- (8n – 18) = 14 – 10(2n – 3) %3D 2

A: We have to simplify the given expression.

Q: Find the sum. (5y + 4) + ( – 2y + 6) =

A: Solution: The objective is to find the sum

Q: MT BF due to tr 2 exp (tr/0.390) 9.6X1018)x 250x106 x1 tz 0:34Ne → TrE 14:99 x 151((p. ftip.fiop)…

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Q: (x+2)2 dx (x+2)3 +C (A + 2x+4 In x +C +4x +4 In x + C (x+2)3 D -In x +C 3. B.

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Q: Subtract the binomials. On simplifying (-3y2 − 8) − (-5y2 + 1), we get y2 − .

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Q: (3x-2)20 (1) find the first 3 terms (2) find the coefficient of x10

A: topic - binomial expansion

Q: Find the coefficients of a* in (6 – ½a)6 and kª in (3k – 21)¹2

A: We have to find the coefficients of a4 in 6 - 12a6 and k4 in 3k - 2l12 . Note that,       a - bn…

Q: 6x-1 If Зх +7 was written in the form 2+ 3x+7 then b%= (1) -1 (3) 12 (2) 7 (4) -15 21 3. 4.

A: Given  6x−13x+7

Q: S (x + 7)dx 15x²+x-2 A. In 2 (3x-1)3 (5x+2) +C B. In 3 (3x-1)2 (5x+2)3| +C C. ln (3x-1)³ || (5x+2)3…

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Q: Evaluate f(2x² + 3x + 1)5 (8x + 6) dx

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Q: (x+2)(x+ 1) y = 2x-4 (2x +3)(2x – 4)– 2(x² + 3x + 2) (2x – 4)? O a.

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Q: Which of the following is a false statement? In the expansion of (a +b) the coefficient of a b° is…

A: We have to choose the false statement.

Q: E[2A+ 3B + C – E + 2D] |

A:

Q: Find the sum. (s³ – 2s – 9) + (2s² – 6s³ + s)

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Q: Find the 7th term of 2+ 2 Write the 5th term of (x + y)1º.

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Q: Find Re(2) if z(4 +) -z+ (80 + 96)

A: In the given question we have to find Re(z) if…

Q: 1. Find the 4th term of y (*- 2y*) using the Binomial Theorem.

A: The solution are next step

Q: 10) (n + 4)

A: (a+b)2 = a2 + b2 + 2ab (n+4)2 = n2 + 16 + 2 × n × 4             = n2 + 8n + 16

Q: Calculate (5xy + 4e²) dS, where S is the triangle with vertices (0, 0, 3), (1, 0, 2), and (0, 4, 1).…

A: Given

Q: (A) I = and (B )I = . Find 2A D - BD O O O none of the above

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Q: Question 11 .2. What is the factorization of x*-8x + 16? (x² +4)Cx² – 4) A. .2 B. (r + 2)(x – 2) %3D…

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Q: а. (4D + 1)(D — : с. (D — х)(D + х)

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: e (t + 5t- 2)

A: Given, e2tt3+5t-2. The given function is can be written as, e2tt3+5e2tt-2e2t, By applying Laplace…

Q: 8a2+9+1 Simplify the following rational expression: 2+3z+2 2-2 (8z + 1)(z + 1)² (x – 2)2 (8x + 1)…

A: To simplify

Q: 5. Simplify the following expressions. a) 3x + 2(5x –7) b) –8n – 8(-4 – 2n) c) k + 1 – 4(2k – 9) -

A:

Q: 12x +1 dx. (2x- 1)2 (3x+2)? Evaluate: 1 (A (2x- 1)2 (3x +2)² +C B (2x- 1)3 (3x + 2)3 3 + C ⓒ In…

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Q: find the coefficient of t8 in expansion of 2t(3+t)20

A:

Q: n+5n  In its simplest form

A: n+5n    In its simplest form is

Q: Find the 11th term of a GP, 2nd term being (b2 – c2) and the 5th term is (b+c)(b – 4)4.

A: I am attaching image so that you understand each and every step.

Q: Draw the Direct form 1 and Direct form 2 of the ff: y(n)=5x(n)+3x(n-2)+4x(n-3)+y(n-1)+5y(n-2)

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Q: 22 - z - 20 22 - 4z – 5 Simplify: 22 + 9z + 20 22 + 7z + 10

A: the given expression is: x2-x-20x2+9x+20÷x2-4x-5x2+7x+10 we have to simplify the given expression.…

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.