Use the second Taylor polynomial P₂(x) for f(x) = x² + ln(1 + x) about æ = 0 and evaluate ƒ ƒ(x)dx. 0 OOO O O 56 - FONO N4/09

Q: let f(x)= X be 1 213 (-√5 < X<√) Y.V Pind P{/X/7/1.5},

A:

Q: For which value of x does the Maclaurin polynomial Tn satisfy Tn(x) = f (x), no matter what f is?

A:

Q: Given the functon /(x) Suppose that the Newton's interpolating polynomial P,(x) of f(x) at the…

A:

Q: Let a E K and let f(x) E K[x]. Prove that the remainder when f(x) is divided by x – a is ƒ(a).…

A:

Q: Calculate L6 for f(x) = v6x + I over [1,3]. %3D (Give your answer to three decimal places.) L6 =

A:

Q: the error estimate for Taylor polyno

A:

Q: Calculate L6 for f(x) = √6x + 3 over [1,3].

A:

Q: 2#Find the the Taylor's polynomial P2(x)for the function f(x)-4x²e 2x about xo-and hence find…

A: The given question has been solved in step 2.

Q: 5. Find the polynomial P2(x) that approximate the function Ax)=sin(x) over the interval [0, 7/2].…

A: Here we use Newton's Divided Difference.

Q: Use the Newton-Raphson iterative to find the root of the function f(x) = 2 Sin (X)-X²+1 in the…

A:

Q: Let P(x)=20x*-7x3 be the Lagrange interpolating polynomial that approximates a function f over the…

A: Given that P(x) approximates a function f over the interval -1, 1, where P(x)=20x4-7x3is the…

Q: If the function f(x)=e* is approximated by Lagrange polynomial P3(x) that interpolates f at 4 points…

A: Linear interpolation is achieved by constructing the lagrange polynomial p3 of order 1 , connecting…

Q: Approximate F(x) throughout the given interval. F(x) = 6° e t/²dt, [0, 1] a. Use the first 3…

A: Given :-  The appropriate Fx throughout the given interval. F x  = ∫0x e-t22 dt  ,  0 , 1 To…

Q: If you use the second Taylor polynomial of f(x)=√x centered at x = 1 to estimate √1.1 as √1.1=1+…

A: We have to find the error by the Taylor's series method.

Q: Q4. Use Newton forward-difference formula and construct appropriate interpolating polynomial and…

A:

Q: Let f(x) = 1.26x* -x² + 1.85x² + 1.32x – 3. Determine the approximate root with at most 15% error…

A:

Q: (b) Construct the Lagrange polynomial. y=sir interpolation. the for function y=sinak taking points…

A:

Q: Let xo < x1. Find a second degree polynomial P(x) such that P(xo) = fo, P(x1) = f1, and P'(xo) = fó-

A: Consider a second degree polynomial in x as: P(x)=ax2+bx+c                                     ..(1)…

Q: Let f (x) = 2x + 3. Compute R6 and L6 over [0, 3].

A:

Q: Use the Newton-Raphson iterative method to find the root of the function f(x) = x³ + x² + 4x + 3 in…

A:

Q: Given: g(x) = e+tan ¹x if x < 0 [1 − x] +3ª_if 0 ≤ x < 2 3x²+4 3x - x2 if x ≥ 2. 4. Find the…

A: We have to find the equations of all horizontal asymptotes for the given function g. The following…

Q: Let P, (x) be the Legendre polynomial of degree n. Show that for any function, f(x), for which the…

A:

Q: A rectangular electric burner plate of the region 1 ≤ x ≤ 3,-≤ x ≤ is heated so that the temperature…

A: Given: It is given that a rectangular burner plate of the region 1≤x≤3, -π4≤x≤π4, is heated so that…

Q: Let f(x) = = a) 9x +4 following. Simplify if possible. f(x) = f(a) a - X = . Evaluate the 4 A' for x…

A: The given function fx=x9x+4. We have to simplify the expression fx-fax-a and find the value of A.

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1 Construct a Langrange Interpolating polynomial of…

A: The given question is solved below

Q: Use the third Taylor polynomial P3 (x) for f(x) = x + x ln x about o ƒ(2). 1 and evaluate

A: Given function is fx=x+xlnx. We have to evaluate f2 by using the third Taylor polynomial P3x for…

Q: Suppose that Pr[A]=8/13, Pr[A|B]=5/7, and Pr[B|A]=5/8. Find Pr[A′|B′]

A:

Q: 1. Consider the function f(x) = x³ + 3x (a) Find the second Taylor polynomial T₂(x) for f(x) based…

A:

Q: For the function f(x)=e*cos(x). let xo = 0₁x₁ = 1, and x₂ = π/2. Use the Lagrange interpolating…

A:

Q: Q1) Find the second Taylor polynomial P₂(x) for the function f(x) = ex cos x about xo = 0.

A:

Q: Let P(x) = 20x* - 7x³ be the Lagrange interpolating polynomial that approximates a function f over…

A: Sol: Px=20x4-7x3Since it approximate the function -1,1Approximation of ∫-11fxdx mus t be equal to…

Q: Q2. Construct a 3rd order polynomial to approximate f(x) = e*sinx for 0≤x≤π/2 the find the exact and…

A: The given function is, f(x)=exsinx. Construction of 3rd order polynomial by using Maclaurian series…

Q: -Find Taylor or Maclaurin for the following functions: 4) f (x) = x³ – 2x + 4 at a = 1

A: