The series converges to e x for all x. a. Find a series for (d/dx)e x .

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? 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.

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Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

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The series converges to e x for all x. a. Find a series for (d/dx)e x .

Question:

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

Step by Step Answer:

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

Thomas Calculus Early Transcendentals

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