Working with Taylor Series

Composition and substitution

Multiplication and division

Approximations with error certification

Limits by series

Which operation produces the series for e^(-x^2) from the exponential's Maclaurin series?

The series for tan x is obtained by which manipulation of the sine and cosine series?

To evaluate lim x to 0 of (e^x - 1 - x)/x^2 by series, what does one read from the exponential's expansion?

Machin's formula pi/4 = 4 arctan(1/5) - arctan(1/239) was historically used for what?

A reciprocal series 1/f(x) expands in powers of x at the origin when which condition holds?

The Cauchy product of sum a_n x^n and sum b_n x^n has x^n coefficient sum over k of a_k b_(n-k). As a single letter, what is the summation index? Answer with a lowercase letter.

Substituting 2x into a series of radius R gives the new radius R/2. For R = 2, what is the new radius? Answer with a number.

A reciprocal series 1/f expands at 0 when f(0) is nonzero. As a single word, what condition? Answer in lowercase.

Composing two series, expanding f(g(x)) as a single power series, is best described as what?

The error function's series comes from integrating e^(-x^2), whose expansion is the exponential series with -x^2 substituted. As a two-word name, what function results? Answer like answer key.