The series

converges to e^x for all x.

a. Find a series for (d/dx)e^x. Do you get the series for e^x? Explain your answer.

b. Find a series for ∫e^x dx. Do you get the series for e^x? Explain your answer.

c. Replace x by -x in the series for e^x to find a series that converges to e^-x for all x. Then multiply the series for e^x and e^-x to find the first six terms of a series for e^-x · e^x.

Transcribed Image Text:

ex = 1 + x + + + + +...