Prove the conjecture bn= 2(bn-1)+1, n>=3 using strong induction. Recurrence is given bn=3bn-1-2bn-2 and b1=1,b2=3

Q: 5. Assume that f is diff on R s.t. f(0) = 0, ƒ(1) = 1, ƒ(2) that 3x € (0,2) s.t. f'(x) = (hint: MVT…

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Q: . Give a recursive definition of each of these sets of ordered pairs of positive integers with…

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Q: Let A = {x + iy : x 0}. Determine the set of all z for which A. (Hint: this is {z : Re() 0}. Find…

A: Set of Z found.

Q: 10. Let f be a continuous function with period 27. If f is an even function (that is, ƒ(x) = f(−x)…

A: The function  is continuous  with period and  is even that is Given  Claim:  for every .

Q: P.) Consider the topology r = {GCR: 0 € G or G=0} on R. Is [0, 1) compact in (R, 7)? Explain why.

A: Given, topology  on defined by, Consider the open cover of  in (Since,  is open set in  for every…

Q: (c) In the previous year, at Hub Motors ltd, for a particular model of Mercedes, Nissan and Ford,…

A: Given that, in the previous year, at Hub Motors ltd, for a particular model of Mercedes, Nissan and…

Q: Prove that f(x) = x³ + x/2 is C¹-structurally stable.

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Q: a. Sketch the region of integration, D, for which y=√x (4x+10y) dA= (4x+10y) dy dx. y=? 2-0 y=z b.…

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Q: S Use a Taylor polynomial with 4 nonzero terms to estimate 0 Estimate = Now estimate the error of…

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Q: Note that you must answer all parts of this problem to receive any credit. [41] 21 H [₁]. Is w a…

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Q: Several oil companies are jointly planning to build an oil pipeline to connect several southwestern,…

A: Given information:Given a network of 10 cities in the southwestern, southeastern, and midwestern…

Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

Q: The system of first order differential equations: has solution: yı(t) Y₂(t) = = [3₁ 13/12 = = -8…

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Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 20 inches above the…

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Q: b. C. L{t² cos(71)} L s-9

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Q: Problem: G Let's verify that gravity is conservative (F is just a force field) and then find the…

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Q: Consider the system of equations. x₂-3x, +1.9=0 and x₂+x²-3.0-0 The next iteration values for x and…

A: Given as,

Q: Determine if v = ? Add Work Check Answer 8- 1 is an eigenvector of the matrix A = [3 0 0 -2 -4 -3 6…

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Q: Solve the system of Differential equations by the matrix method dx2 dx dt dx3 dt =-3x3 -=-X₁ + X₂ +…

A: since you have posted multiple questions, we will provide the solution to only first question as…

Q: Calculate P(FIE), if P(E|F) = 0.1 P(E) = 0.92 P(F) = 0.19 Round your answer to five decimals.

A: We have to calculate .

Q: In x x→ x-1 25. Find lim " ln x In x given that log₂ (x+1) ≤· -≤1-— as x⇒1¯¯. x-1 X

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Q: #6: Use the Laplace transform to solve the following initial value problem, y"8y'-9y= S(t-4), y(0) =…

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Q: Suppose a subspace is spanned by the set of vectors shown. ((-24].[23]) Find a basis for the…

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Q: Let a₁ [4] 9 āz DNE Is b a linear combination of a₁ and a2? and Ob is not a linaer combination of a₁…

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Q: Four gallons of gas cost $13.70. Write a unit rate that fits with this statement for 1 gallon, you…

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Q: #2. Given vector field F = (x² + y² - z², x²y,3z) and the box-like surface S surrounding the solid…

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Q: Solve the initial value problem y" + 4y = -12 sin 2x, subject to y(0) = 1.8 and y'(0) = 5.0

A: We have to solve the initial value problem.

Q: 4. As a tornado moves, its speed increases. The function S(d) = 93 log d + 65 a) Graph this…

A: Given information:Function representing the speed of wind near the center of a tornado: , where  is…

Q: 4. In the usual topology again, is locally compact? 5. Deduce. {(0, 0)} U {(x, y) = R²; x >0}

A: The given set is, .Locally compactness means that each point in the set has a compact neighborhood.

Q: Determine whether or not the following games are fair. (a) 42 [43] This is a fair game. This is not…

A: Determine whether or not the following games are fair.If payoff matrix is , then the expected payoff…

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure:

A: Here is the problem. the limits of x and y of the given triangle.As x limits we have from 0 to 4.Y…

Q: You are reviewing data collected on TV sales in three different branches of your electrical retailer…

A: We have three sites, each with their own data on 'Data Collection Time' and 'TV Sales'.Specifically…

Q: Consider the following set of data, I m = Number 1 b = Number 1.7 2 2.8 3.6 4.3 Y 294 (Again, round…

A: For the given data, we have to fit the function  for some constants NowWhere

Q: payoff matrix for a game is given by -2] pute the expected payoffs of the game for the pairs of…

A: We will find the expected payoffs.

Q: radioactive element decays

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Q: 3. Display an argument to show that the Gamma Function is defined for s> 0. = 6²°0 e-p₁-1α dt T(s) =…

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Q: 1. Consider a function f(x) = x² + x² 3 2 4x - 4. (a) Compute the minimum number of iterations…

A: Given Information:The function is given as .Objective:c) Find the exact roots of the function…

Q: A table of values of an increasing function f is shown. X f(x) 10 lower estimate upper estimate 14…

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Q: 6. Given tan (0 - 450) = 4, find tan 0. D

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Q: Given that g(x) + 7x sin(g(x)) = 35x² + 24x − 35 and g( ² ) = 0, find g'( ² ). g ( ½¾7 ) =

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Q: Q(x₁, x2, x3) = x² + x² + x² + 4x₁x2 − 2x13 subject to x1+x2+x3 = 0 and -x₁+x2+x3 = 0, Q(x, y, z) =…

A: To determine the definiteness of the quadratic forms subject to the given constraints, we can use…

Q: Given vector field F = (x + tan-¹(yz), 2y - 8e12xz, 4z3 - 10 ln(2x+y)). S is the surface defined as…

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Q: 1 Find a fundamental matrix of the following system, and then apply x(t) = Þ(t)Þ(0)¯ ¹x。 to find a…

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Q: Exercise 1. Use the Maclaurin series of tan-¹(u) tan ¹ (u) =U- to approximate the definite integral…

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Q: #6. Use Stokes's Theorem to evaluate , curl F n dS where S is the surface z = 4 - x² - y², z≥ 0 and…

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Q: pply the theorem L(f* g) = L(f)L(g) to find the inverse Laplace transform; also do it in mother way…

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Q: Problem: Use either Stokes' theorem or the divergence theorem to evaluate the following integral in…

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Q: Use de Moivre's Theorem to find the following. Write your answer in standard form. [2(cos 10° +isin…

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Q: Kate, Ron and Lisa play on the same soccer team. Kate has played 20 minutes in total. Ron has played…

A: Kate, Ron and Lisa play on the same soccer team. Kate has played  minutes in total. Ron has played…

Q: that the amounts of time (in minutes) required for assembling the frames, installing the wheels, and…

A: Given information:Time required for assembling frames, installing wheels, and decorating for…