Consider the function f(x) = ax + b, where a and b are constants. Which of the following is one of the two possible values of f(-1) if (fo f)(x) = f[ f(x) ] = 4x - 9? Show your in your solution sheet which will be submitted to the bin. O -3 O 1 O 7 -7 cannot be found on th e othor choicos

Q: 5) Find the general solution by using reduction of order method to (x² + 1)y" – 2xy' + 2y = 0 given…

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Q: 1 Solve the f (x)= X²_3X+1 =0to find %3D of a) by- using fixed-point the Value Iteration), Assume Xo…

A: Since you have asked multiple questions, we will solve the first question for you.  If you want any…

Q: Let f(x) = x³ – 2x – 6. Tell why f has a solution in [1, 3], and use the Newton-Raphson method with…

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Q: Perform one iteration of the Newton's method to minimize the function f(x1,x2) = 2(x2 – x?)² + (1 –…

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Q: Q2) The critical points of the function F(x,y) = x + 3xy + y3 O (0,5) O (1,0) none of others O (1,1)…

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Q: Find the x -value of the point on the curve y=V/2x+2 that is closest to the point (8,0). x=6 O x= O…

A: To Determine: find the x-value of the point on the curve that is closed to the point (8,0) Given: we…

Q: Find the coefficient of X^35 in the generating function (x^4+x^5+x^6+x^7+x^8)^5 (Show work and…

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Q: 4. Suppose the following functions are a general solution of: y(4) + a3y/" + azy" + a;y' + a0y = 0

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Q: Let y : R →R be the real-valued function defined on the real line, which is the solution of the…

A: Ans:-  Initial value problem: y'=-xy+x,  y=0=2          solution : y'+xy=x, 40=2          is of…

Q: Q.4. Determine the negative root of: f(x) = x' – x² - 5x – 3 using the most suitable Newton-Raphson…

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Q: ind the solution to the eguation 2x² – In-- 5x = 0. Use a tolerance of function error of 0.001| 3x…

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Q: 3.Eliminate the arbitrary constant on the given equation: xsiny – x²y-3 = C

A: In this question we have to eliminate the arbitrary constant on the given equation.

Q: The function h(x) given by h(x) = –6 – 8.2944x - 4/5x + 3.84x³ has a critical number c = = -1.2.

A: We have given function hx=-6-8.2944x-45x5+3.84x3 and critical number c=-1.2

Q: Q1 Find root of equation f(x) = In (x')-5, using N-R method in [5,6] with e S0.0001, take E=|x1-x,…

A: Note: It is assumed that the N-R method is the Newton-Raphson method. The root of the equation…

Q: A Ⓒ Using integration by parts to solve f √4x²+k -2√4x²+k -√4x²+k 2√4x²+k x³ dx √4-x² and letting u…

A: Let's find.

Q: The next iterative value of the root of x² – 4= 0 using the Newton-Raphson method, if the initial…

A: Newton-Raphson method: It is one of the most widely used numerical methods for the approximate…

Q: Estimate one real root of f (x) = 0.95x3 - 5.9a2 + 10.9x - 6 using three iterations of Newton…

A: Given function is  f(x)=0.95x3-5.9x2+10.9x-6 we have to estimate one root using the Newton-Raphson…

Q: 1) A function f (x) can be linearized around x provided that 8x is very small f(x + 8x) = f(x) +…

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Q: Q-2: For what values of a, m and b does the function: 3, f(x) = -x² + 3x + a, 0<x <1. (mx + b, 1<x<…

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Q: I) Find solutions to the following function f(x) = 3x + In(x) using five iterations of the…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find a particular solution y, of the following equation using the Method of Undetermined…

A: Given differential eqution y''-y'-2y=3x+3

Q: Find a particular solution y, of the following equation using the Method of Undetermined…

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Q: 6.Suppose that the joint p.m. f. of X and Y is X- 00 Yə -1- 09 10 Determine: (1)-The value of a;…

A: Given:     x y   0 1 2 -1 0.05 0.1 0.1 0 0.1 0.2 0.1 1 a 0.2 0.05

Q: •1 1 g(x) = dt 2x In(t + 1)

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Q: For f(x) = x³ - x +4, compute the formula for n+1 in Newton's method. - In +4 - 3h - In 3a급-1 | In +…

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Q: The function f(x) = X = (6x 3) e5 has one critical number. Find it.

A: Given function ,   f(x)=(6x-3)e5x

Q: Given 2.3 f (x) = +1, 2+ sin(ræ) that is defined over [1, 6] with a step (h= 1). Using the divided…

A: Given f(x) = 2x32+sinπx+1f(2) = 2(2)32+ sin2π+1 = 162+0+1 = 8+1 = 9f(3) = 2(3)32+ sin3π+1 =…

Q: The Existence and Uniqueness Theorem guarantees that the solution to (t+ 2)y"-sint y+ e2t у-1) - о…

A: Given differential equation is :  (t+2) y'' - sint y' + tt-4y = e2tt ,  y(-1) = 0

Q: e 2t * – 3x + 2x = e2t+1

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Q: 5. Show that the formula for the Secant method can be written in the form xn+1 = [f(xn)xn-1…

A: Secant Method: Consider, y = f (x). Let, x0 and x1 are two initial approximations for the roots of f…

Q: 4. Prove that if f(x) = agx" + a,x"-1 +..+ an-1x = 0 has a positive root x = xo, then the equation…

A: Note that f0=0 and that fx0=0. So using mean value theorem there must be some 0&lt;λ&lt;x0:…

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Q: Find the x values of the two critical points of: 3(x- 1)23 6x – x² - 5 if x > 2. if x < 2 f(x)%3D X…

A: we have the given function is ;  f(x)=3(x-1)2/3if x≤26x-x2-5if x&gt;2

Q: Prove that any solution of the equation 1 + x = 0, t> 2 has a zero on the interval [2īn, 27(n + 1)]…

A: Strum Comparison Theorem-  Let p1,p2,q1,q2 be the real valued continuous function defined on the…

Q: Also p; 2 0 for all j = {1, ., k} and E-1P; = 1. What is the value of E(X) and V(X)?

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Q: he function f(x) = e – 1 is to be solved using lewton-Raphson method. If the initial value of o is…

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Q: Q3M) Given the IVP x²y' +2xy = cosh x, y(1)=0: a) Determine the explicit solution by providing and…

A: Since we only answer one(first) of the multiple question from the given multiple no. of question.…

Q: 5. Let a > 0, find the "generalized solution" to a" + 3x' + 2x = 8(t – a) with x(0) = 1 and æ'(0) =…

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Q: 3. Which of the following functions, 2 x(t) = 1, x(t) = ²/₁ is a solution to the DE x'= -x²? x(t) =…

A: As per our guidelines we are allowed to solve only 1 complete question. kindly repost others. THANK…

Q: The function f(x)=(7x−7)e^4x has one critical number. Find x.

A: Given,          fx=7x-7e4x

Q: The Newton-Raphson method fails if Of" (x₂) = 0 Of (1₂) = 0 O f' (1₂) = 0 0 = (º¹),f O

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Q: Suppose that we don't have a formula for g(x) but we know that g(1) = -4 and g'(x) = V x2 + 15 for…

A: g(1)=-4, g'(x)=x2+15 Finding the value of g '(1) g '(1)=12+15=1+15=16=4

Q: Suppose * = f(). (a) Given y(xo) = Yo, when does this equation have a unique solution? = z(x, y) to…

A: Given- Suppose dydx = fymx To find-  Given yx0 = y0, when does this equation have a unique…

Q: 5) Find the general solution by using reduction of order method to (x2 + 1)y" – 2xy' + 2y = 0 given…

A: Use the procedure of reduction of order to solve the given differential equation as in next step.

Q: 3) Find the general solution by using reduction of order method to ty" – (t + 1)y' + y = 0 given…

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Q: 24 Show that the solution of equation satisfying the condition O T-0, as t0 (1) T-0, for x-0 and x=a…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Given G(x) = jin(2t+1)dt , find G '(x). O In(2x + 1) O In(2x + 1) - In3 O In(2t + 1) + C 2 2x+1

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Q: Given that n2 1 and xn =V 4n² + 3n – 2n Will {Xn}, be divergent or convergent? n=1 Will E-1 Xn be…

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Q: Solve the following linear independent and Wronskian. 2. Are the functions y, = e* and y2 = x…

A: Here we have to determine whether the given functions are linearly independent.  We have,  y1=ex…

Q: The function f(x) = (6x+5)e^4x has one critical number. X= ?

A: Proceed as shown below...