Using Neville’s Method - Value of the Polynomial Interpolating the Points - Mathematics Assignment Help

Assignment Task :

Give all answers to 6 decimal places and keep as many digits as your calculator will keep for intermediate calculations. If an answer is exact (e.g. integers, 1/4,...) you do not need to write all 6 decimal places.

You may not use a computer or spreadsheet on this exam. You may, if your calculator has one, and you know how to use it, use the table app.

Unless stated otherwise, each problem is worth 25 points. (The exam is out of 200 points total.)

You must show all work to receive any credit!!!

1: Using Neville’s Method, find the value of the polynomial interpolating the points (−4, 4), (−1, 3), (0, −2), and (5, 4) at the value x = 3.141593.

2: Find the Newton form of the polynomial interpolating the points in problem 1 above.

i: Use the trapezoid rule to estimate the value of the integral.

ii: Use the error formula to find a bound on the error.

iii: Compare the actual error to the error bound. Does the error lie within the error bound? If not, explain why.

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