3. In this problem, you will explore Taylor polynomial approximations for et and use these to come up with estimates for the value of e. (a) Find the degree 1, 2, 3, 4, and 5 Taylor polynomial approximations for e centered at 0. (1) That is, each coefficient should be a simplified fraction. If you are not able to easily simplify your coefficients by hand, here's a good chance you've made a bad decision along the way. After all, our primary goal is to get a simple approximation hat we can calculate by hand. (b) Graph your five Taylor polynomial approximations together with ex. (2) If you've done this cor- rectly, you should see that, as the degree increases, the Taylor polynomial approximations get closer to the original function e, at least near the center (x = 0). (c) Use the degree 5 Taylor polynomial approximation to approximate the value of e; give your answer as a decimal. (Do a reality check: is your approximation pretty close to e?)