Skip to main content\(\newcommand{\N}{\mathbb N}
\newcommand{\Z}{\mathbb Z}
\newcommand{\Q}{\mathbb Q}
\newcommand{\R}{\mathbb R}
\newcommand{\unknown}{{\color{gray} ?}}
\DeclareMathOperator{\arcsec}{arcsec}
\DeclareMathOperator{\arccot}{arccot}
\DeclareMathOperator{\arccsc}{arccsc}
\newcommand{\tuple}[1]{\left\langle#1\right\rangle}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Chapter 9 Power Series (PS)
Learning Outcomes
How do we use series to understand functions?
By the end of this chapter, you should be able to...
Approximate functions defined as power series.
Determine the interval of convergence for a given power series.
Compute power series by manipulating known exponential/trigonometric/binomial power series.
Determine a Taylor or Maclaurin series for a function.
Readiness Assurance.
Before beginning this chapter, you should be able to...
-
Compute limits.
-
Express the sum of indexed values using summation notation.
-
Employ the ratio test for convergence.
-
Power rule for differentiating and integrating.
