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: in²3xdc O 3x-sin3xcos 3x +C O 3x+sn3xcos 3x +C Bx-sn3xcos 3x 3x-sn 3rcos3x +C 3x+sn3xcs Bx +C

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Q: 512x 1-x -3 - =—1 find volue of Σ(x²)"=? n=1

A: Given that the equation 512x1-x-3=-1   .

Q: JUX² +2x-8 dx Evaluate lx + 1Wx + 1)* + 9 = l(x + 1) + Vtx + 1}² – 9|]+c 9ln (+ 1)/(x + 1)² – 9 –…

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Q: 3. Determine a and b for Y X1 and Y2aX bX2 such that EX1 EX2}= 0, Var(X) Var(X2) Var(Yi) Var(2) 1,…

A: The provided information is:

Q: 2.24 Derive the simplest sum-of-products expression for the function f(x₁, x2, x3, x4) X₁ X3 X4 +…

A: we have to derive the simplest sum-of-products expression for the functionFor the given function,…

Q: A water tank has the shape of the solid formed when the region bounded by y = and the y-axis for 0 <…

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Q: 21 _) P') pludx= чи (и+1) сеn+ л 2 и+31 и+1

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Q: The integral 2a12 + 5x° is equal to -dx 3 x5 + x3 +1 (a) -25 + C (2) +2² + 1)* (b) z10 +C (1 + کے +…

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Q: Let B = {1-3t +t² , 2 - 5t + 3t2, 1 + 5t2} and p (t) = 2 – 5t + 4t. Find x [p]g. %3D X1 = X2 = X3 =…

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Q: en-3h-S If y= show that day (on-3)* 2n-3

A: Given function is  y=ex^2-3x-52x-3                           ⋯1 To show:…

Q: Show that if (B) (C) N N then the value of neither x nor y can exceed 1/4. (A) N = X, 2x, = 3x and…

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Q: a) 6e2x – 17(e*) + 12 = 0 b) 82x+1 = 45-x %3D

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Q: 16) n = 4; 2, 1 and 3 + 3i are zeros; f(1) =78 %3D

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Q: By the Fundamental Theorem of Calculus, Part 1 4 ["* vi(2+1)dt = ["^(2√²+11) de dt 4 - = ( 5 -t² +…

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Q: 3. find the Lem and hef of 12,15 andh 2kyapplying the pacene factoce. eatial mothod 2x 2x 3 3 X5 2…

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Q: show that 11 1+ 1 n-1 1 n(ā-μο)2 Σ=1(xi-x)2 n/2 n(ā – μο)2 Σ=1(α; - z)2 (xi

A: We need to prove that:

Q: 3. Find the sum of all values of k such that 2k k -dx =15. (A) 3 (B) 2 (C) 1 (D) 0 (E) 1/2

A: ∫12kx-kx2dx=15∫12kxdx-∫12kkx2dx=15∫12kxdx-k∫12kx-2dx=15x2212k-kx-2+1-2+112k=15x2212k-kx-1-112k=15x22…

Q: 3. Evaluate the integral / Vr+3 (x- 1 4 4 (a) 극(z +3)72-(r + 3)52 + 국(2 +3)%2 +C 1 4 (b) (r + 3)"…

A: This question is related to Indefinite integration, we will solve it using given information.

Q: B/Determine: s²+95+2 1.2-[ (5+3)(8-1)2 2.2-1 [ 词 8+1 ((x-1)82)

A: We have to find the inverse Laplace transform. 1. L-1s2+9s+2s+3s-12 2. L-1s+1s-1s2

Q: Q.4) Find the value of Sigma (d=sum of student id + 22, and c=12) 4c(d + x)(7c* +2cz +9z*) ((d +x)*…

A: As the student ID is not provided, I assume the sum of the digits are 10 (say). Then d=10+22=32 and…

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: If gcd( m,91) = gcd(n, 91) = 1 %3D %3D

A: Given, if gcd(m, 91)=gcd(n, 91)=1,  To prove that                     91|m37-n37

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…

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Q: 5z2+2z+1 dz Rzl<2_ (z-i)³ 1z|<2

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Q: 1. 3Y4 + 3Y5 + 3Y6+ ...+ 3Y15 2. (Xg — 4) + (X, — 4) + (Х10 — 4) + (X11 — 4) 3. (X3Y3) + (X4Y4) +…

A: To write in summation notation  1): 3 y4+3y5+.......3y15  2): (X8-4)+(X9-4).........(X11-4)  3):…

Q: 1(会) %3D Evaluate. Assume u > 0 when In u appears. 9) [x8x9 - 4)4 dx 16x37 16x 15624 256) dv 26 16x…

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Q: 3x -1 (x² – 1)? (as a partial sum) Select one: a. A B X-1 x +1 b. B A x -1' (x– 1)² x +1 (x + 1)² С.…

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Q: 2011- 2) Let T C T-¹(a+bx+cx² + dx³) = = 2a +(-2) b + 1c + (-1)d + (-7a+ 0b + 1c +(-3) d) x + (2a +…

A: Inverse Linear Transformation if TT-1(x) =T-1(T(x))=x.

Q: If F=(x^2+y^2+z^2)^n (xi +yj+zk) then V.F is

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Q: In Exercises 1-8, find the power series solution to the initial value problem. 1. y' + y = 0, y(0) =…

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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.