Exploration 3 A Series with a Curious Property Define a function f by a power series as follows: f ( x ) =1+ * + x2 + + + . . .+ + ... 2! 3! 4! n! 1. Find f'(x). 2. Find f(0). 3. What well-known function do you suppose f is? 4. Use your responses to parts 1 and 2 to set up an initial value prob- lem that the function f must solve. You will need a differential equation and an initial condition. 5. Solve the initial value problem to prove your conjecture in part 3. 6. Graph the first three partial sums. What appears to be the interval of convergence? 7. Graph the next three partial sums. Did you underestimate the interval of convergence