It is the goal of the instructor that the students will be able to:
apply the properties of geometric series.
differentiate, integrate, or substitute into a known power series in order to find additional power series representations.
use derivatives to find the Maclaurin series or Taylor series generated by a differentiable function.
approximate a function with a Taylor polynomial.
analyze the truncation error of a series using graphical methods or the Remainder Estimation Theorem.
use Eulers formula to relate the functions sin x, cos x, and
. use the nth-Term Test, the Direct Comparison Test, and the Ratio Test to determine the convergence or divergence of a series of numbers or the radius of convergence of a power series.
use the Integral Test and the Alternating Series Test to determine the convergence or divergence of a series of numbers.
determine the convergence or divergence of p-series, including the harmonic series.
determine the absolute convergence, conditional convergence, or divergence of a power series at the endpoints of its interval of convergence.
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Correction Sheets