1 The cubic Legendre polynomial is P2(x) = (5x³ – 3). Prove that it is orthog onal (over [-1, 1])) to all polynomials of degree 2.

Q: 1. Consider y-f(x)=cos(2x)+x² over [0, 3t/2]. (By hand but use a calculator) a) Use the three nodes…

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Q: 10. If a Taylor polynomial of f (x) = In In (x – 1) can be used to approximate In1.2, what should be…

A: Given: fx=lnx-1  ……1   To find: Centre of Taylor expansion for ln 1.2

Q: A cubic epline Ss defined by (2(G)% 3(x-1)+24-1) -(x-1) 5.(x) = 4 + 4(x – 2) –(+– 2)² +=(x - 2)* S…

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Q: Find the nth Taylor polynomial centered at c. f(x) = In(x), n = 4, c = 3 P4(x) = Need Help? Watch It

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Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at a = 8 for f(x) = In(x +1). %3D

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Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at x = a for f(x) = 28 sin(x), a =…

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Q: Find the Taylor polynomial of degree four for the function f(x) = In (1 - 10x) at x = 0. The Taylor…

A: Fourth order Taylor polynomial

Q: 1. If f(x) is an nth-degree polynomial and Pn(x) is the nth Taylor polynomial for f at x 0, what is…

A: Given  If f(x) is an nth-degree polynomial and Pn(x) is the nth Taylor polynomial for f at x 0 we…

Q: 15. Find a polynomial P(x) of degree < 3 for which P(1) = y2 P'(1) = y2 P(0) = y1, P'(0) = y, with…

A: cubic polynomial is of form y=ax³+bx²+cx+d

Q: 2) FIND THE TAYLOR POLYNOMIAL 13 (x) foR THE FUNCTEON f CENTERED AT THE NUMBIER a . TOU ON -4x flx=…

A: f(x)=xe-4x, centre at a, where a=0

Q: Find the Taylor polynomials p-. Ps centered at a = 0 for f(x) = 9 e

A: Answer and explanation is given below

Q: O is Cos x about x The second-degree Taylor polynomial for f (x) = 1-x

A: The second degree Taylor polynomial of a function f(x) at x=a is given by…

Q: Find a monic polynomial f(x) of least degree over C that has the given numbers as zeros, and a monic…

A: Given, Zeros, -3i,4 it has three zeros ±3i, 4 these zeros are factor of the equation…

Q: .Find a monic polynomial f(x) of least degree over C that has the given numbers as zeros, and a…

A: Find a monic polynomial f(x) of least degree over C that has the given numbers as zeros, and a monic…

Q: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and…

A: Follow the procedure given below.

Q: (d) The cubic Legendre polynomial is P₂(x) = (5x¹-32). Prove that it is orthog- onal (over [-1,1])…

A: To Prove: The given Legendre polynomial P2(x)=125x3-3x is orthogonal to all polynomials of degree 2…

Q: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and…

A: We know that If a complex number a+ib is a zero of a polynomial, then a-ib is also zero of that…

Q: g(x) = ex²

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Q: Find the Taylor polynomials po, P1, P2 and P3 for f(x) = Inx at x = 1. Use a graphing utility to…

A: Answer :-

Q: 6. Find the nth Taylor polynomial centered at C a. f(x) = x²cos x, n = 2, c = n

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Q: 13 - What is Taylor polynomial with order 3 generated by f(x) = x° + 3x² + 2x + 4 at x = 1.

A: The Taylor polynomial of order 3 is given as follows :

Q: Find the Taylor polynomials p4 and ps centered at a = for f(x) = 8 cos (2x). 12 P4(x) =

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Q: 6. Find the first 4 terms of the Taylor polynomial of f (x) = 1/x centered at x = -2. Show your…

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Q: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and…

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Q: Consider a function f(x) and second its Taylor Polynomial p2(x) centered at a. If p2(x) is not…

A: Given a function f(x) and second Taylor polynomial p2(x) centered at a. Also given maximum of p2(x)…

Q: 1 of 2 For the function f(x) = In (1-8x), find the Taylor polynomials of orders 0, 1, 2, and 3…

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Q: Find the Taylor polynomials p,, ., P4 centered at a = 0 for f(x) = cos (- 2x). %3D P1 (x) =| %3D

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Q: . Find the Taylor polynomial p3 centered at a = 4 for ƒ(x) = 2/x. %3D

A: To find the Taylor polynomial p3 centered at a=4 for the given function f(x)

Q: Consider a function f(x) and its second Taylor Polynomial P2(x) centered at a. If p₂(x) is not…

A: Introduction: The Taylor series representation is very significant application of differential…

Q: 1. Using x, = 1,x1 = 2,x2 = 3, and x3 = 4, find the Lagrange interpolating polynomial of In(x + 1).

A: Given function is f(x)=ln(x+1) Evaluate value of function at given set of points: x 1 2 3 4…

Q: The Taylor polynomial of order 1 generated by f(x)= cos-(x) at a == is Select one: a. 2 P¿(x) = 3 V3…

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Q: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and…

A: Here we need to find the polynomial R of degree 4, R has degree 4 and zeros at (4-2i) and 2 with…

Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at x = a for f(x) = 12 sin (x), a =…

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Q: Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f(x) = In(3 + x) at x = 8. Po(x) =…

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Q: (d) The cubic Legendre polynomial is P2(r) =(5x – 3r). Prove that it is orthog- onal (over [-1, 1)…

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Q: Find the Taylor polynomials p,, .., P4 centered at a = 0 for f(x) = 3 cos (3x) P;(x) = P2 (x) = P3…

A: The given function is fx=3cos3x at a=0. It is required to find the polynomial approximation when…

Q: 13. (a) Find the 3rd-degree Taylor polynomial for the function f(x) = In x centered at a = 1. (b)…

A: The derivative of lnx with respect to x is 1x. The power rule of differentiation states that d…

Q: Find the Taylor polynomial of degree 4 for the function f(x) = In(x), centered at a = the sums of…

A: The derivative of the function is the measure of how fast the function is changing with respect to…

Q: 1. Find the Taylor polynomial p3 centered at a = 7/3 for f(x) = = COS I.

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Q: Find the Taylor polynomial of order 3 centered at 0. 1 f(x) = %3D 5-x x3 p3(x) = 25 125 625 x2 p3(x)…

A: Given: fx=15-x The Taylor series of above function when n=3. Taylor series is given by:…

Q: Calculate the Taylor polynomials T₂(x) and T3 (x) centered at x = a for f(x) = 16 sin(x), a = 플..…

A: Introduction: The formula of the Taylor series polynomial of the function y=f(x) centered at point…

Q: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and…

A: Answer

Q: 2. Find the second degree Taylor polynomial of g(x) = V1– 3x about 3, then use it to approximate the…

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Q: 5. Find the Taylor polynomial of degree 3, p3(), for the function f(x) = Vx, centered at a = 4.

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Q: 2) Find the 3€ Tayler polynomial P,(x) fix) = Sinx at X= -½. 3) Using B,(x) from 2), estimake sin…

A: The formula for taylor series is     where f (k) (a)  is kth derivative of f at given point a.

Q: Find the Taylor polynomials p4 and p5 centered at a = for f(x) = 10 cos (x). 6. %3D P4(X) =]

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Q: 10. Find the Taylor polynomial T(x) centered at a = 1 for (2) = ='/% %3D

A: The general form of a Taylor expansion centered at a of an analytical function f isf(x) =…

Q: Find the Taylor polynomial of degree four for the function f(x) = In (1 – 7x) at x = 0. The Taylor…

A: We hve to find the Taylor polynomial of degree four for f(x) =ln(1-7x) By using Taylor expension

Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at x = a for ƒ(x) = 22 sin(x), a =…

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Q: Show that a polynomial p(z) of degree n is orthogonal to any Legendre polynomial PN(z).where N>n,…

A: The Legendre equation is  1-x2y''-2xy'+pp+1y=0              (i) Eq. (i) can be written as…