prove that and = nd(n)/2

Q: Example 9.10. Solve yn2-4y = n² + n - 1.

A: The solution is given as

Q: 6. i,How many permutations are required to be sure of predicting the outcome of tossing a six sided…

A:

Q: How many iterations is done in order to find the root of the following using bisection method? f(x)…

A: We have given function f(x)=x4-2x3+x2-3x+3 for[0,5]. We need to find number of iteration is done in…

Q: 3. fe2x+Inx² sin x² dx = = 2x -+√e²x cos x² dx

A:

Q: 1.5⁹ Explain why the two graphs in Fig. 1.23 are not isomorphic. Figure 1.23

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Q: O cos 4x + (Dx + E) C) cos 4x + (Dx+ Am Cm 2:

A:

Q: 2. Using the fact that D₁ ((2 − x)−¹) = (2 − x)-², find the Maclaurin series for 4x3 f(x) = (2 -…

A: The given function is fx=4x32-x2 To find: (a) Maclaurin series for fx=4x32-x2            (b) radius…

Q: 3.8 The integral 28x³e-x² dx is approximated by Simpson's 3/8 rule with 9 intervals. Let f(x) =…

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Q: Use mathematical induction to prove и исин) {i= VEN 2 1 = 1

A:

Q: Q1) which of the following sequences is converge or diverge: {m} } . J 10n

A: We want to check the convergence of given sequences.

Q: J 2 3 ув-у'-6y=0 y" +2y'= у"+3y"-4y'=0 О

A: According to our guidelines, we are supposed to answer only first three subparts.Kindly repost other…

Q: 2. Given the matrix A below, 1 A = 02 2 1 0 1 2 0 1 4 solve for det inv A. The several of the…

A:

Q: f(x,y) 3 - x² + 2x - y²

A: We have given functionf(x,y)=3-x2+2x-y2. We need to find the domain of given function, sketch the…

Q: [MO23] For the function y = cos x + sinx, determine its a. MacLaurin Series expansion up to fifth…

A: Given : The given function is ;  f(x) = cosx + sinx To find :  (a) Maclaurin series expansion up to…

Q: Example 8.19. Use Romberg's method to compute dx 1 + x² correct to 4 decimal places.

A: Let y = 11+x2  and let I = ∫01dx1+x2take h = 0.5 =12The tabulated values of y are   x0 x1 x2 x…

Q: Use the first derivative test to find the location of all local extrema in the interval (0, 10) for…

A:

Q: now that Reis Banach f|xl|= | ( 2 | ², 1² ) / 2 j=1 and vector space. 2h is complete.

A: We have given Rn andx=(∑j=1n  ξiq. We have to show that Rn is Banch space, vector space and…

Q: Determine the value of z in the below equation, giving the answer in the form x + yi. z-8=i (7-2z)

A: Solution

Q: 13. For the following digraphs, determine ISI, the cardinality of S if: a) S is the transitive…

A: A={a,b,c,d,e} The given relation as R={(b,c), (b,e), (c,e), (e,b), (e,c), (d,a)} For transitive…

Q: For the following linear system, find the inverse of the coefficient matrix using Gaussian…

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Q: Consider the plane region to the right. Using Simpson's 1/3 rule (2 intervals), Estimate the area of…

A: Make a table as follows x 0 1.2 2.4 f(x) 1.5 1.8 1.5 Area using Simpson's rule is given by…

Q: Determine the values of r for which the given differential equation has solutions of the form y = t"…

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Q: Solve yn+2 - 2 cos ayn+1+yn = cos an.

A: First we need to write equation in symbolic form then solve.

Q: What are the strongly connected components of the digraph below? Your answer should consist of a…

A: A graph is said to be strongly connected if every vertex is reachable from every other vertex. The…

Q: Find the solution of the equation P №²₂ a²z อ + cos y ax² ay ² which tends to zero as x→∞ and has…

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Q: 5. Find all values of k for which A is invertible. [k A=0 Lk -k 3 k+1 1 -8 k-1.

A: As per guidelines I have solved the first question i.e.questions no.5 if you want solution of other…

Q: Use Squeeze Theorem to evaluate lim x44x COS X logix

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Q: Find the factor group G divides H where G is the quaternions,H=Z(G)

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Q: 5. Use variation of parameters to find a general solution of the system, x'(t) = Ax(t) + f(t), where…

A: We have to find the general solution of the given problem.

Q: Objective function: z = 2x + y Constraints:     x  ≥  0     y ≥ 0 2x  +  3y ≤ 60 2x  +  y ≤ 28 4x  +…

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Q: fe²x+Inx² sin x² dx = +√e²x cos x² dx

A:

Q: Suppose f is continuous everywhere, f’ is differentiable everywhere except at x = -1, and the graph…

A: Here we use the property of symmetrical function.

Q: 2. Specify on which intervals is f increasing/decreasing and where the graph of f is concave…

A: Given is information about the function f(x), f'(x) and f''(x) Then, to specify the intervals where…

Q: Prove that the subgroup {o ES5o (5) = 5} of S5 is isomorphic to $4.

A: The given question is related with abstract algebra. We have to the subgroup σ ∈ S5 | σ5 = 5 of S5…

Q: Test the convergence of the power series below: (-2) n Σ 3n-2(3x-5)n n=1

A: Radius of converges of the power series

Q: 13. Compute 41023 (mod 11). a. 14. Prove that for any integer n, n31 = n(mod7).

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Q: What is the missing number? * 15 17 1 9 8 12 27 40 00 00 28 12 23 13 ? 28

A:

Q: Matrices D, M and X are 5 x 5 invertible matrices. Given det (A) = 7, det (M) = -4, and Hlet (P) = 6…

A: (a).  det3MT As  detMT = detM So det3MT = 35detM = 243(-4)  =  -972 Hence Answer: det(3MT) = -972

Q: III. Use Squeeze Theorem to evaluate lim 8478 COS X log x

A: To Evaluate: limx→+∞cosxlog12x by using squeeze theorem:

Q: 1. Given: f(x, y) = y a. Find and sketch the domain of the given function b. Find and sketch the…

A: Directional derivative of a function f(x,y,) in the direction of unit vector…

Q: Number of voters 14 14 11 11 9 I. Head-to-head total score: X: vs. Y: II. Head-to-head total score:…

A: Solution :-

Q: too ·00 dx COSX x² +hx+5 =le Residue solution cos (2)

A:

Q: Q2): A polluted lake has an initial concentration of a bacteria of (1*10' part/m³), while the…

A: Given that,The differential equation that governs the concentration (C) of the pollutantas a…

Q: 3. Let p= (1,2,-1) and h= (0.1,0.2,-0.1). For each of the differential 1-form w: R³ → C (R³, R)…

A: Please find the solution in next step

Q: Notation: Definition and Examples. Expand your answer.

A: Definition- Notation is a symbolic system for the representation of mathematical items and…

Q: PROBLEM: Derive the z-transform for f(t) = sin oot u(t). z¹sin(@T) ANSWER: F(z) : = 1-2 z ¹ cos(@T)…

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Q: .Using 1 - node Gaussian integration, we have f f(x) dx ≈ w₁f(x₁). What is the value of x₁ ? b+a (a)…

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Q: Find the divergence and curl for the following vector fields. Describe the characteristics of the…

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Q: X đẻ cosxu sinh x) X=1.5 Secant method secant method of optimization

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Q: Simpson 1/3 rule for integration is mainly based upon the idea of (a) Approximating f(x)in I=ff(x)dx…

A: We need to find the idea behind Simpson  13 rd rule.