Share
Explore BrainMass

Maclaurin Series, Lagrange Interpolation Polynomial and Newton's Interpolation Formulas

1.Expand the following function into Maclaurin Series (see attached file) using properties of the power series.

2. The Lagrange interpolation polynomial may be compactly written as is a shape function. Sketch the shape function in a graphic form.

3. Write a forward and backward difference Newton's interpolation formulas based on the following data. Interpolate the values of y at x = 1.3, 2.5, and 2.7.

x y
11.302
21.616
31.954

4. Find the root of the following transcendental equation by the numerical method of your choice

5. Find the following integral by the trapezoidal rule and by the Simpson's rule. Find the theoretically predicted errors. Compare to the exact value. Explain the results.

Attachments

Solution Summary

Maclaurin Series, Lagrange Interpolation Polynomial and Newton's Interpolation Formulas are investigated.

$2.19