1. Let's do some explorations with approximating ex. Ultimately, we want to approximate e^(23.5 ).
2. (a)Compute the second degree of the Taylor polynomial of ex centered at x = 0. Let's call it T(x).
3. (b)When is err(x) = |e^x T (x)| < 0.1?
4. (c)Give the value for ln(10)? Let's call that a. What is ea?
5. (d)Compute 23.5. Let M be the integer part of that fraction. Compute out d = a 23.5 M a, both roughly and accurately.

(e)Compute 10^M and T(d). How does this relate to e^(23.5)? best to explain the relationship. This is the key.

(f)Compute e^(23.5) directly with a calculator and compare to the previous item.