Chapter 1: Q18P (page 41)
Find the sum of each of the following series by recognizing it as the Maclaurin series for a function evaluated at a point .
Short Answer
The sum of the series, i.e. ,
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Chapter 1: Q18P (page 41)
Find the sum of each of the following series by recognizing it as the Maclaurin series for a function evaluated at a point .
The sum of the series, i.e. ,
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Find the following limits using Maclaurin series and check your results by computer. Hint: First combine the fractions. Then find the first term of the denominator series and the first term of the numerator series.
Use Maclaurin series to evaluate each of the following. Although you could do them by computer, you can probably do them in your head faster than you can type them into the computer. So use these to practice quick and skillful use of basic series to make simple calculations.
at x=0 .
Use Maclaurin series to evaluate each of the following. Although you could do them by computer, you can probably do them in your head faster than you can type them into the computer. So use these to practice quick and skillful use of basic series to make simple calculations.
.
Find the values of several derivatives ofat t = 0. Hint:Calculate a few derivatives (as functions of t); then make the substitution, and use the result of Problem 24(f) or 25.
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