Suppose we want to approximate the function f(x) = sin(x) on the interval [0, 1] by using polynomial interpolation with xo = 0, 21 = 0.5, and x2 = 1. (a) Let pi(x) be the polynomial that interpolates f(x) at ro and 2₁. (i) Find the error bound at x = 0.3 (i.e., the bound for error f(0.3) - p1 (0.3)). (ii) Find the error bound on the whole interval [0, 0.5]. (iii) Use any method of your choice to find p₁(x) and compare the actual error at x = 0.3 with the error bounds in previous steps.
Suppose we want to approximate the function f(x) = sin(x) on the interval [0, 1] by using polynomial interpolation with xo = 0, 21 = 0.5, and x2 = 1. (a) Let pi(x) be the polynomial that interpolates f(x) at ro and 2₁. (i) Find the error bound at x = 0.3 (i.e., the bound for error f(0.3) - p1 (0.3)). (ii) Find the error bound on the whole interval [0, 0.5]. (iii) Use any method of your choice to find p₁(x) and compare the actual error at x = 0.3 with the error bounds in previous steps.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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![1. Suppose we want to approximate the function f(x) = sin(x) on the interval [0, 1] by
using polynomial interpolation with xo = 0, x₁ = 0.5, and x2 = 1.
(a) Let pi(x) be the polynomial that interpolates f(x) at xo and ₁. (i) Find the
error bound at x = 0.3 (i.e., the bound for error f(0.3) - pi(0.3)). (ii) Find the
error bound on the whole interval [0, 0.5]. (iii) Use any method of your choice
to find p₁(x) and compare the actual error at x = 0.3 with the error bounds in
previous steps.
(b) Let p2(x) be the polynomial that interpolates f(x) at xo, x1 and 2. (i) Find the
error bound at x = 0.3. (ii) Find the error bound on the interval [0, 1]. (iii) Use
any method of your choice to find p2(x) and compare the actual error at x = 0.3
with the error bounds in previous steps.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c842333-6f00-4a4b-9f61-7bda344711a4%2Fcdee350e-0186-4119-8caa-fd74d75b4d58%2F2md8th_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Suppose we want to approximate the function f(x) = sin(x) on the interval [0, 1] by
using polynomial interpolation with xo = 0, x₁ = 0.5, and x2 = 1.
(a) Let pi(x) be the polynomial that interpolates f(x) at xo and ₁. (i) Find the
error bound at x = 0.3 (i.e., the bound for error f(0.3) - pi(0.3)). (ii) Find the
error bound on the whole interval [0, 0.5]. (iii) Use any method of your choice
to find p₁(x) and compare the actual error at x = 0.3 with the error bounds in
previous steps.
(b) Let p2(x) be the polynomial that interpolates f(x) at xo, x1 and 2. (i) Find the
error bound at x = 0.3. (ii) Find the error bound on the interval [0, 1]. (iii) Use
any method of your choice to find p2(x) and compare the actual error at x = 0.3
with the error bounds in previous steps.
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