Section 10.17
Applications of Series
Impossible integrals? Difficult limits? Computers calculation? Taylor series solve problems that algebra cannot.
1
Integration
has no elementary antiderivative.
Expand as a series, then integrate term by term!
2
Worked Examples
1. The Impossible Integral
Integrate as a series.
Substitution
. Let ..
Integrate
.General Term: .
2. Limits
.
Expand Numerator
..
Divide
.3. Estimation
Estimate .
Maclaurin Series
.Calculate
.Actual is . Close!
5
Practice Quiz
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