Chapter 8: Q. 50 (page 692)
You were asked to find the Taylor series for the specified function at the given value of . In Exercises 45-50 find the Lagrange's form for the remainder
, and show that
on the specified interval.
Solution will be provided later
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Use an appropriate Maclaurin series to find the values of the series in Exercises 17โ22.
Complete Example 4 by showing that the power series diverges when .
Why is it helpful to know the Maclaurin series for a few basic functions?
Let be a power series in with a positive and finite radius of convergence . Explain why the ratio test for absolute convergence will fail to determine the convergence of this power series when or when .
What is meant by the interval of convergence for a power series in ? How is the interval of convergence determined? If a power series in has a nontrivial interval of convergence, what types of intervals are possible?
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