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Chapter 8: Q. 8 (page 692)
Given a function f and a Taylor polynomial for fat , what is meant by the nth remainder ? What does measure?
For each point , there is atleast one c between such that,
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If m is a positive integer, how can we find the Maclaurin series for the function if we already know the Maclaurin series for the function f(x)? How do you find the interval of convergence for the new series?
Find the interval of convergence for power series:
Let f be a twice-differentiable function at a point . Using the words value, slope, and concavity, explain why the second Taylor polynomial might be a good approximation for f close to .
In Exercises 23–32 we ask you to give Lagrange’s form for the corresponding remainder,
Let be a power series in with a finite radius of convergence . Prove that if the series converges absolutely at , then the series converges absolutely at the other value as well.
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