Question 2 Use mathematical induction to prove that n(n+ 1)(2n + 1) 6 i=1 for all integers n > 1.

Q: Find all eigenvalues and eigenfunctions of the following e X"+ XX = 0, X (0) = X'(2) = 0.

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Q: SorvE THモ CONGROEモNしE 626 X Rエ mod5

A: As 5 is an odd number, by fermat's theorem, we have             x5-1 = 1 (mod 5)           => x4…

Q: Given the geometric progression Find the sum of the first 9 terms of the sequence. 7, 35, ...) 25 5…

A: Given GP is 725, 75, 7, 35, ...

Q: b) Consider the following Linear Programming problem: Min z = 2x, – 3x2 Subject to 1 1 z* +2 54 X1 +…

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Q: OLet W, X, Y, and Z be invertible square matrices. Show that if WY = YW, then det Y det(W Z –YX)

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: Given:  r(t) = F(t) + G(t)  Where F(t) = cos t i - sin t j + 6 √t k G(t) = 2 cos t i + sin t j…

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 1/3x^3/2,…

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Q: Find the volume of the region using cylindrical coordinates.

A: Volume is the amount of space occupied by the closed surface. In this problem, the region is bounded…

Q: find whether the kectas linecoly depadent Justiy Your (5 -1 4),(6 t5),(169) independet? aue 94swer .

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Q: 91 a) Find an equation of the sphere with center (1,-3,-5) and tangent to xz-plane.

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Q: g statements are helpful- prem 3.59

A: Yes

Q: Evaluate the following integral using three different orders of integration. (xy + z?) dv, where E =…

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Q: . Show that there exists a real number 0 <x< 2 so that x' + 8x² – 10 = 0 -

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Q: (1) [4+4 points] Determine whether the following series converge or diverge: k! (a) Σ 2.4.6... (2k)…

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Q: roblem 5: calculate: lim | sin" rdr

A: To calculate: limn→∞∫-11sinnxdx

Q: Find the solutions of the system of inequalities by graphing: x + y 2

A: The region shaded by both inequalities is the solution of the system of inequalities.

Q: Cluster sampling is a form of convenience sampling in which the population elements are selected…

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Q: Verify Green's theorem for F =, where C is the part of the parabola y = x², and the line y = 4 for…

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Q: Which of the following is false? O A p-series is convergent ifp> 1. O None of them. 5 n The series…

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Q: b)I,- ;: Use the Comparison Test to test the series .7 Σ 2 + n° n=1 for convergence or divergence.

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Q: Find the area of the region outside the cardioid r = 2 – 2 cos 0 and %3D inside the circler = 4.…

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Q: 12. x Ct) = cosh 3t Sin 3t te

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Q: Find the Maclaurin series for f and identify its interval of convergence. Evaluate f(1804) (0),…

A: We have to approximate the f(0.1). And sum of series.

Q: Let f : R? → R be defined by f((x, y)) = 9x – 7y. Is f a linear transformation? a. f((r1, Y1) + (x2,…

A: It is given that the function f : ℝ2→ℝ is defined by fx, y=9x-7y. We have to check whether f is a…

Q: Payment of $882 due 1 month ago and $498 due today are to be repaid by a payment of $400 one month…

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Q: Question no. 3 Use the inversion algorithm to find the inverse of the matrix (if the inverse…

A: Q3 asked and answered.

Q: Derive the conclusion using Rules of Inference. 3æ N(x) Væ (N(x) → I(x)) :. Bx I(æ) 1. Statement…

A: We have to derive the conclusion using the Rules of Inference.

Q: Approximate the following functions using Taylor series. Solve the absolute and relative error in…

A: To find the Taylor's polynomial of a function f(x) at x=a and the error, use the following formulae.…

Q: Evaluate: > Si(0.5)-1

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Q: Prove that if f, g :R → R are continuous at x E R, then ƒ+gis continuous at x E R as well.

A: By using the definition of continuous function this above statement can be easily proved.

Q: Assume thatf is differentiable in (-oo, x) and af'(r)N 0 for all a E (-00, 00). Prove that f has the…

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Q: 5. Identify and sketch the graph of the following equations in R. (a) a2 + 2y2 + 22 - 8r + 12y - 2:…

A: We have to sketch the graph of the given functions of three variables x, y and z in the three…

Q: 4 k 2 -5 9 0 -4 -1 -9 -2 Let A = 0 0 k -4 6 0 0 0 2 6. 0 0 0 0 4 choose When is det(A) > 0? >

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Q: Find the eigenvalues A1 < A2 and associated unit eigenvectors ū1, ū2 of the symmetric matrix A = The…

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Q: 18 Two forces, of magnitude p newtons and q newtons, have a resultant of 2V7 N when they act at 90°…

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Q: a) Find the magnitude of the resultant of the forces (2ị – 3j)N, (4i + j)N and (-3i + 3j)N. b) Two…

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Q: [1 2 1 21 21 2 1 et A = 1 2 1 2 [2 1 2 1. (a) (b) (c) Find all eigenvalues of A. Find a basis for…

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Q: 24. Which is the recursive definition of the set of positive integers that are multiples of 4? * aj…

A: We have to find the correct option which represents the set of positive integers that are multiples…

Q: Apply the alternative form of the Gram-Schmidt orthonormalization process to find an orthonormal…

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Q: 27. List all vertices that are adjacent with vertex A.{Note: Type the answer WITHOUT space. Separate…

A: We have given a graph .with vertex set ,  V = A , B , C , D , E. We know that , if two vertices in a…

Q: In each part, find 121. 12. Z = -3 – 4i 13. z = -7i V3. 1 = Z 14.

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Q: The general solution of the differential equation 81.x² y" + 81xy' + (81x² – 25)y = 0 is? Check all…

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Q: x2 Y2 F.n dS = S

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Q: x²-x dx 1+3x²-2x³

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Q: t も c6 10. XCt)> { -8 + -8 t ct-6)? » t >6

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Q: Rojana is 8 years older than AJ, and the sum of their ages is less than 24. Find their possible…

A: We want to find possible ages of Rojana and AJ.

Q: Approximate the following functions using Taylor series. Solve the absolute and relatice error in…

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Q: Let -2 2 2 -6 A = -2 -2 2 -6 Find the dimension of the kernel and the dimension of the image of the…

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Q: Question no. 3 Use the inversion algorithm to find the inverse of the matrix (if the inverse…

A: Q3 asked and answered.

Q: 8. Given the statements "People who are red/green color blind cannot distinguish between green and…

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