Exercises

1. Use the procedure involving the solve command to find the quadratic Taylor polynomial approximation to with base point . Plot your approximation on the same graph as .
2. Use the Taylor command from the CalcP package to generate the quadratic Taylor polynomial approximation to the function from the first exercise. Use the same base point. Verify, graphically or otherwise, that the two quadratic polynomials are the same. You might find the Maple expand command useful.
3. Fill in the details of the proof of Theorem 1. That is, show that the formula in the theorem satisfies the conditions in Definition 1.
4. Suppose you wanted to approximate the function over the interval with an absolute accuracy that is less than . That is, you want to choose a base point a in this interval such that the quadratic Taylor polynomial approximation to with that base point satisfies for . Find a base point a that works. Include a plot that demonstrates this.