Taylor and Power Series: How to Solve Problems
In this chapter, we’ll look at how to solve four different classes of problems involving Taylor series, Taylor polynomials and power series:
• how to find where power series converge or diverge;
• how to manipulate Taylor series to get other Taylor series or Taylor polynomials;
• using Taylor series or Taylor polynomials to find derivatives; and
• using Maclaurin series to find limits.
Let’s say we have a power series about x = a:
As we saw in the case of geometric series, a power series might converge for some x and diverge ...