Let 1 5-1 A = 0 1 0 and P = 0 0 0 15-2 05 Given that P diagonalizes A, then compute A¹¹. i A" i i

Q: [ (ax + b) c+b) dx = ○ / (ax + b) ² + C O O4a ¹ª (ax + b) ² + C O4a (ax + b)² + C O4 (ax + b) + C 7a

A: You must have basic idea about indefinite integral in order to understand this better.

Q: 3) V12-b+4= 6

A: #3 Given,   12-b+4=6

Q: xdx 3 (5–4x-x2) Z

A: We have to evaluate the integral

Q: 5. Determine the combination V x (Vf) given that X" + y"

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Q: (b) 2+4+6++ (2k) = k² + k and 1+3+5+ ... + (2k − 1) = k² (k = 1,2...).

A: Alternative Interpretations and Solutions: 1. Verification by Substitution for Specific Values of…

Q: 11. Find MZJHI. K (3x + 2) (12r - 17)°

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Q: :: Find L-1 5+7 \s+7/

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Q: b) f(x) = x* + 29x² + 100.

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

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Q: 3a + 46° – 5 = 3 (6) +4(2) – 5 ? ||

A: Solution: The objective is to calculate the value

Q: Use the substitution method to evaluate V1-22dx

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Q: Divide x+2 x²+3x-10 x²-2x-8 x+3

A: We know that the divided can change multiplication then numerator and denominator are change…

Q: /(r² – 8)5

A: Use substitution method to find the integral

Q: 1. Let -1 3 [1 2 3] A = 2 1 4 [1 2 3] 0 1 2 -4 1 and C 2 1 -3 Find the following: (a) 24 (b) 2АB (c)…

A: Solve by matrix operations

Q: Question 2 Give the form of a particular solution of y" - 8y' +16y=-2xe 5e4-2. -2z - a) z = = (Ar² +…

A: We have to find Particular solution for given Differential equation  y" - 8y' + 16 = -2xe-2x - 5e4x…

Q: (5) {1,2} C P({1, 2}).

A: Given  set is {1,2},  we knew that power set of a given set is set of all subsets of the given set.…

Q: a) 1 (x-1)(x+2)(x+4)

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Q: Find x, y, z, and w. X = y = Z= W = x 7 (2x y 6 - 5) (2x = ¹) ] - [ (²x - ² 9y Z 9 By + 8) ] 8 (w +…

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Q: 2. Find (w + 1)(w-w+1).

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Q: 10. (3k2- 2k + 5) + (-2k² + 6k -7)

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Q: Let A = {a, b}, B = {x, y}, C = {x, z}. а) (6.1 #32b) Find P(A x B). a

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Q: 3(z+5)=12

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Q: find The Six Solutious of The eq- 6 Z+27+2

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Q: 3y² + 5y - 8

A: The given quadratic equation is:  3y2+5y-8

Q: 2. Show that if 8=(AB)- then - > N - - (AB)² + (aß)² – (αB)² – (AB)² = [(A) − (α)] [(B) − (ß)] +…

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Q: Compute a (х + 2) dx. O x3 + x² + C O x² (x² + 2x)+C x2 + 2x ) + C 2 - + C 2 + x2 + C 3

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Q: 11 (d) 12/13 + (1 1/12 - 11/1/1)

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Q: Let ged(a, b) = d then which of the following is correct @ dla (i) dlb (i) dl(ax + by) (a) only (i)…

A: gcd(a,b) = d