Using series you know from Chapter 1, write the power series (about the origin) of the following functions. Use Theorem III to find the disk of convergence of each series. What you are looking for is the point (anywhere in the complex plane) nearest the origin, at which the function does not have a derivative. Then the disk of convergence has center at the origin and extends to that point. The series converges inside the disk. sinh z
Using series you know from Chapter 1, write the power series (about the origin) of the following functions. Use Theorem III to find the disk of convergence of each series. What you are looking for is the point (anywhere in the complex plane) nearest the origin, at which the function does not have a derivative. Then the disk of convergence has center at the origin and extends to that point. The series converges inside the disk. sinh z
Using series you know from Chapter 1, write the power series (about the origin) of the following functions. Use Theorem III to find the disk of convergence of each series. What you are looking for is the point (anywhere in the complex plane) nearest the origin, at which the function does not have a derivative. Then the disk of convergence has center at the origin and extends to that point. The series converges inside the disk.
Determine whether the series is absolutely convergent, conditional convergent or divergent. Make sure
to show detail step by step solutions. Make sure to name the test that you are using to do this problem,
example: integral test, comparison test, alternating series test, root test, etc.
n=1
(−1)n-³
√n
Find the series' interval of convergence and, within its interval, the sum of the series as a function of ?x.
A: rewrite the function as an expression which includes the sum of a power series
B: modify your expression above by expressing the sum as a power series
C: determine the radius of convergence of your power series above. Show steps
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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