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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