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Chapter 8: Q. 66 (page 702)
Use the results from Exercises 51鈥�60 and Theorem 7.38 to approximate the values of the definite integrals in Exercises 61鈥�70 to within 0.001 of their values.
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Let be a power series in with a finite radius of convergence . Prove that if the series converges absolutely at either , then the series converges absolutely at the other value as well.
What is Lagrange鈥檚 form for the remainder? Why is Lagrange鈥檚 form usually more useful for analyzing the remainder than the definition of the remainder or the integral provided by Taylor theorem?
In Exercises 49鈥�56 find the Taylor series for the specified function and the given value of . Note: These are the same functions and values as in Exercises 41鈥�48.
Complete Example 4 by showing that the power series diverges when .
Use an appropriate Maclaurin series to find the values of the series in Exercises 17鈥�22.
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