2 [n(n+1) Using induction prove that 1³ + 23 + ... + n³ = for n > 1. 2

Q: (a) Consider the real linear map T : R' - R', expressed as follows: (1 2 -1 49 -1 X1 X1 + 2x2 - x3…

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Q: :Q2 Find F(t) for the differential equation below x²y' + 2xy – 2y = 0

A: Introduction:   A differential equation is an equation that contains the derivative of an unknown…

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Q: erential equations, use phase flow, ial conditions, indicate x and y Iclines and equilibria. (if…

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Q: 8.1) Using rules of logs show that if y= ab' then log y = log a + tlog b 8.2) Consider 91=10'. Using…

A: According to guidelines we solve three subparts.thanku

Q: (b) у" — 4у'+ Зу %3D Зе2х + 4е* + 2e3х

A: Given differential equation: y''-4y'+3y=3e2x+4ex+2e3xTo find: General solution of the differential…

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Q: ANBANBA' O B A'N B'

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Q: .9. Which is true for a nonempty subset S of R? O If S is nonempty and sup S exists, then S is…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

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Q: Show that f(2) = (2-1) cos) singue has an essential z + 2 at 2=-2

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Q: В C -21 72 57 65 29 G 16 84 AO 33 -19- 91 25 81 47 102 F

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Q: What is the 109th term of the arithmetic sequence (963, 936, 909, 882, ..)?

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Q: Exercise 6.1.4 Consider (6.1) and (6.2) in the case that ka = 4, kg = 1, ke = 3, and g(t) = 0. The…

A: Given: The system of differential equations, u˙Pt=-4uPt+4uTt u˙Tt=uPt-4uTt The initial conditions:…

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Q: (a) Compute the Fourier sine series expansion of f(x) = 3x – x² on [0, 3]. %3D (b) To what value…

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Q: Determine which conclusion is based on deductive reasoning. * iA person must have a vaccination…

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Q: - 3 - 1 Let y = -6 u = - 5 u2 = Find the distance from y to the plane in R' spanned by u, and uz. 5…

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Q: 5) Let Xbe an arbitrary space and let J, and I be two topologies on 1 2 it. (i) Is T, U T always a…

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Q: Find all the roots of the given function. Use preliminary analysis and graphing to find good initial…

A: Given the function is  fx=4lnx-x2+6x-3

Q: List the ordered pairs in the relation R from A ={0,1,2,3} to B = {0,1,2,3} where (a,b) ϵ R, if and…

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Q: a, = -2a,-1 + 24a,-2 for n > 2 with initial conditions ao = 3, a = 4. The solution is of the form:…

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Q: s (x) In (1t x2) 74.8

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Q: List the ordered pairs in the relations on {1,2,3} corresponding to the matrix, [1 0 = 10 1 1 11 1.

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Q: 9. Which is true for a nonempty subset S of R? * If S is nonempty and sup S exists, then S is…

A: We want to find true option.

Q: (I + u)u] 2 induction prove that 13 + 23 + ...+ n³ = , for n > 1. 2.

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Q: You want to save P900 per quarter for 3 years towards the purchase of an appliance. You feel that…

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Q: m An = {-: m e N}, ne N, n where N are non-negative integers. What is lim inf A, and lim sup A,?…

A: To find the lim sup and lim inf of the given sequence An .

Q: . Using Jacob Iteration, solve 10 -2 -4 -2 X1 -2 6 -2 X2 4 -4 -2 10 X3 Start with x1(0)=1, x2(0)= 1,…

A: Given, 10-2-4-26-2-4-210x1x2x3 = -24-1 start with x0(0)=1,  x2(0)=1, x3(0)=0 we have to find the…

Q: 15. Verify Stokes' Theorem for the vector field F = 2xyi + xj + (y + z)k and the surface z = 4 – x²…

A: please comment if you need any clarification. If you find my answer useful put thumbs up. Thank you.

Q: Let T: P2 that is, 7. > P2 be the linear operator T(p(x)) = p(2x+ 1), T(co+ C,x+ C,x²) = c, + c,(2x…

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Q: 6. Which is is true for any set S of real numbers? * S has a least upper bound. S has a greatest…

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Q: he statement "All of us are OK and all of them are losers." is an example of* O negation )…

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Q: in fuzzy graph theory what is the CONN And give examples

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Q: Using a method of reduction to separable equation and reduction to linear equation, find the general…

A: According to guidelines we solve one question.thanku

Q: Let ? and ? be permutations on the set {1,2,3,4,5,6,78,9}, defined as follows

A: Introduction: A permutation is a bijective mapping from a set to itself. The general way to…

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Q: 4. For his dream car, Enzo invested $18 000 at 7.8% interest, compounded monthly, for 5 years. After…

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Q: B) Find the limits by using L.Hopital rule : 7x 1. lim 0 sin 2 -16 2. lim 4 (V+5)-3

A: 1. Here limx→07xsin 2x is of 00 form, so by applying L. hospital rule, we get limx→07xsin 2x =…

Q: Assessment 3 Directions: Decide whether each of the following is a proposition or not a proposition.…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

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A: Given: The network flow as follows: To find: The general solution of the network flow. To find: The…

Q: what is the symmetric difference ? And give examples

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Q: an 34an-1 – 289an-2 for n > 3 with initial conditions aj = 68, az = -1734. an

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Q: 4. Find a general solution of the linear system. x' = 2x + y = x + 2y – e2t

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Q: Write v as the sum of two vectors, one in Span fu,} and one in Span fu2,u3,u4}. Assume that fu1 .u4}…

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Q: Time Is the following statement true or false? The graph of y= S f(t)dt, where f is a piecewise…

A: given that,  The graph of y=∫0xftdt,   where f is the pieces-wise constant function, as shown in…