1.Let f(x)= e' and x = [-1, 2].a. Find an upper bound for the error in the MacLaurin polynomial of degree five.b. If we want the error to be smaller than 0.0001, what degree MacLaurin polynomial is needed?C. If we use a MacLaurin polynomial of degree 5 and we want the error to be less than 0.0001,what interval restriction would we need to have for x?

Answered: 1. Let f(x)=e' and x = [-1, 2]. a. Find…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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a. Find the second Taylor's polynomial P,(x) of the function f(x) = cos z about the point to approximate cos 42° (use 4 digit rounding) (3 marks) 6 b. For a function f(x) the forward differences are given by 2o = 4 f[ro] = 52 f(ro, 21] = 9 21 = 5 flæ1] =? f(ro, 21, x2] = 1.5 f[x1, x2] =? 12 = 6 f[x2] =? Find the missing entries in the table. (3 marks)
3.please help
2. Find y at x = 0.3, using 2-degree Newton Polynomial. Show table of divided differences using 3 points x = 0, 0.2, 0.4. Show polynomial used.
6. For f(x) = 2x - x, construct the second Lagrange interpolating polynomial using the nodes xo = 1, x₁ = 1.25 and x₂ = 1.6. Then approximate ƒ(1.4) and find the absolute and relative errors.
1. Let f(x) = 2x2 – x – 1 and let g(x) = x – 1 Which statement is true? A. One root of f (x) is -1. B. g(x) is a factor of f (x). C. One root of f (x) is 2. D. If f(x) is divided by g(x), the remainder is 2.
. Let ƒ(x) = (x² - 4)³. Do the following. (a) Find the maximum value and the minimum value of f on the interval [-1,3]. (b) For what value of c such that -1 ≤ c ≤ 3 does f attain its maximum value?
Q2) The following values of the function f(x) = sin x + cos x are given X 10⁰ 20⁰ 30⁰ 1.3660 f(x) 1.1585 1.2817 Construct the Lagrange interpolation polynomial that fits the data and find (), compare with exact values.
Kk.340.
1. For function f(x) = x² ln x, let x₁ = 1, x₁ = 2, and x₂ = 3. Use divided difference al-gorithm to construct Newton's interpolating polynomial of degree three (call it Q₂(x)). Compare Q(x) with P(x) in HW4 problem 2, does this violate the uniqueness property of interpolating polynomials?
6. a) For the given function (x) = V1 - x, let x, = 0, x1 Lagrange's polynomial P2(x) of degree at most 2 to approximate f (0.55). Use 3-digit rounding. = 0.4 and x2 = 0.7. Construct a %3D b) Find the absolute error.
c,d,e needed
6. For f(x) = 2x - x, construct the second Lagrange interpolating polynomial using the nodes xo = 1, x₁ = 1.25 and x₂ = 1.6. Then approximate ƒ(1.4) and find the absolute and relative errors.

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