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Chapter 1: Q8-3-14P (page 1)
Using (3.9), find the general solution of each of the following differential equations. Compare a computer solution and, if necessary, reconcile it with yours. Hint: See comments just after()3.9, and Example 1.
14.
Hint: For Problems 12to 14, solve forx in terms of y.
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(a) Using computer or tables (or see Chapter Section ),verify that,and also verify that the error in approximating the sum of the series by the first five terms is approximately .
(b) By computer or tables verify that
the sum of the first five terms is
(c) Prove theorem . Hint: The error is .
Use the fact that the absolute value of a sum is less than or equal to the sum of the absolute values. Then use the fact that to replace all by , and write the appropriate inequality. Sum the geometric series to get the result.
Use power series to evaluate the function at the given point. Compare with computer results, using the computer to find the series, and also to do the problem without series. Resolve any disagreement in results (see Example 1)..
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