1.Expand the following function into Maclaurin Series (see attached file) using properties of the power series.
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.
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.
Maclaurin Series, Lagrange Interpolation Polynomial and Newton's Interpolation Formulas are investigated.