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In this lesson, we will learn how to represent exponential and trigonometric functions as power series, find the expansion around zero, and find the interval of the series convergence.

Q1:

Consider the function .

Find .

Find , where represents the th derivative of with respect to .

Hence, derive the Maclaurin series for .

What is the radius of convergence of the Maclaurin series for ?

Q2:

What are the first four derivatives of with respect to ?

Write the general form for the th derivative of with respect to .

Q3:

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