2) Consider the inner product (p,q) = p(x)q(x) dx on C[0,1] – the space of functions continuous on the interval [0,1]. Use Mathematica to answer the following problems. a) Construct an orthonormal set from the set {1,x,x²,x³, x², x³}. b) Use the orthonormal set to find an approximation to sin(x). c) Plot sin(x) and the approximation from b.) on the same set of axes over the range 0 ≤ x ≤ 1. d) Compute the metric distance between sin(x) and the approximation from b.). e) Find the Taylor Polynomial of degree 5 for sin(x). f) Find the metric distance between sin(x) and its Taylor Polynomial of degree 5.
2) Consider the inner product (p,q) = p(x)q(x) dx on C[0,1] – the space of functions continuous on the interval [0,1]. Use Mathematica to answer the following problems. a) Construct an orthonormal set from the set {1,x,x²,x³, x², x³}. b) Use the orthonormal set to find an approximation to sin(x). c) Plot sin(x) and the approximation from b.) on the same set of axes over the range 0 ≤ x ≤ 1. d) Compute the metric distance between sin(x) and the approximation from b.). e) Find the Taylor Polynomial of degree 5 for sin(x). f) Find the metric distance between sin(x) and its Taylor Polynomial of degree 5.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.2: Length And Angle: The Dot Product
Problem 70EQ
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![2) Consider the inner product (p,q) = p(x)q(x) dx on C[0,1] – the space
of functions continuous on the interval [0,1]. Use Mathematica to answer
the following problems.
a) Construct an orthonormal set from the set {1,x,x²,x³, x², x³}.
b) Use the orthonormal set to find an approximation to sin(x).
c) Plot sin(x) and the approximation from b.) on the same set of axes
over the range 0 ≤ x ≤ 1.
d) Compute the metric distance between sin(x) and the approximation
from b.).
e) Find the Taylor Polynomial of degree 5 for sin(x).
f) Find the metric distance between sin(x) and its Taylor Polynomial
of degree 5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9ca0fe0-8326-4567-9bb6-5d60d0a741b4%2Fe5d6c7e5-a071-4548-9ef2-43c5f981db49%2Fkv7hkb9_processed.png&w=3840&q=75)
Transcribed Image Text:2) Consider the inner product (p,q) = p(x)q(x) dx on C[0,1] – the space
of functions continuous on the interval [0,1]. Use Mathematica to answer
the following problems.
a) Construct an orthonormal set from the set {1,x,x²,x³, x², x³}.
b) Use the orthonormal set to find an approximation to sin(x).
c) Plot sin(x) and the approximation from b.) on the same set of axes
over the range 0 ≤ x ≤ 1.
d) Compute the metric distance between sin(x) and the approximation
from b.).
e) Find the Taylor Polynomial of degree 5 for sin(x).
f) Find the metric distance between sin(x) and its Taylor Polynomial
of degree 5.
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