Homework 11

Details

1. (8 points) IDAA 11.3.7 (page 410)
   Don't forget to (1) clearly state the decision version, (2) clearly outline the verification algorithm, and (3), justify that the verification algorithm is polynomial-time.
2. (5+2+2+3+2 pts) The Taylor Polynomial of degree n for computing eⁿ is given on page 412 (formula 11.6).
   1. Use it to approximate the value of e^0.25≈1.28402541669... using a fifth-degree Taylor Polynomial (i.e. e^x≈1+x+...+x⁵/5! )
   2. What is the absolute error of this approximation, to at least 10 decimal places?
   3. What is the relative error of this approximation?
   4. According to formula 11.8 on page 413, what is the maximum value of the expected absolute error?
   5. Is the actual error greater than or less than the expected error? Explain why your answer makes sense.