Using the Lagrange interpolating polynomials, estimate f(1.25). What is the actual error at this point? What is the maximum error? Analyze briefly. 2 sentences max. Obtain the Lagrange interpolating polynomial using all the data points below:1.51.0f(x) | 0.8415 | 0.9093 | 0.1411 | -0.7568 | -0.95891.0.52.02.5The data points in #1 satisfy f (x) = sin 2x. Assuming that f (x) = sin 2x is the"theoretical function," plot f (x) = sin 2x against the Lagrange interpolatingpolynomials. Comment on the convergence of the Lagrange interpolating polynomial.(e.g. Is there a range within which it fits well with f (x) = sin 2x? Analyze briefly. 3sentences max) Note: This is for students with gadgets.2.3.Using the Lagrange interpolating polynomials, estimate f(1.25). What is the actualerror at this point? What is the maximum error? Analyze briefly. 2 sentences max.

Note:- As for this problem, part (3) is mentioned for solution so, solution is here for part (3). If…

Answered: Using the Lagrange interpolating…

Using the Lagrange interpolating polynomials, estimate f(1.25). What is the actual error at this point? What is the maximum error? Analyze briefly. 2 sentences max.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 65E

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Question

Using the Lagrange interpolating polynomials, estimate f(1.25). What is the actual error at this point? What is the maximum error? Analyze briefly. 2 sentences max.

Obtain the Lagrange interpolating polynomial using all the data points below:
1.5
1.0
f(x) | 0.8415 | 0.9093 | 0.1411 | -0.7568 | -0.9589
1.
0.5
2.0
2.5
The data points in #1 satisfy f (x) = sin 2x. Assuming that f (x) = sin 2x is the
"theoretical function," plot f (x) = sin 2x against the Lagrange interpolating
polynomials. Comment on the convergence of the Lagrange interpolating polynomial.
(e.g. Is there a range within which it fits well with f (x) = sin 2x? Analyze briefly. 3
sentences max) Note: This is for students with gadgets.
2.
3.
Using the Lagrange interpolating polynomials, estimate f(1.25). What is the actual
error at this point? What is the maximum error? Analyze briefly. 2 sentences max.

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