The document discusses approximating the exponential function ex using partial sums of its power series. It shows the first seven terms of the power series for ex: 1, 1 + x/2!, 1 + x/2! + x^2/3!, and so on up to 1 + x/2! + x^2/3! + ... + x^7/7!. Each additional term provides a closer approximation to the value of ex.

1. AP Calculus BCApproximating 𝑒𝑥 with partial sums of a power series

2. 𝑓𝑥=𝑒𝑥

3. 𝑓𝑥=𝑒𝑥 𝑠1=1

4. 𝑓𝑥=𝑒𝑥 𝑠2=1+𝑥22!

5. 𝑓𝑥=𝑒𝑥 𝑠3=1+𝑥22!+𝑥33!

6. 𝑓𝑥=𝑒𝑥 𝑠4=1+𝑥22!+𝑥33!+𝑥44!

7. 𝑓𝑥=𝑒𝑥 𝑠5=1+𝑥22!+𝑥33!+𝑥44!+𝑥55!

8. 𝑓𝑥=𝑒𝑥 𝑠6=1+𝑥22!+𝑥33!+𝑥44!+𝑥55!+𝑥66!

9. 𝑓𝑥=𝑒𝑥 𝑠7=1+𝑥22!+𝑥33!+𝑥44!+𝑥55!+𝑥66!+𝑥77!