Question: 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

The series ex = 1 + x + + + + +...

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.

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

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a We can differentiate both sides of the series for ex term by term to obtain a series for ddxex dd... View full answer

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