Infinite Sequences and Series (BC Only)

Derivative of $a_n$ with respect to $x$

Indefinite integral of $(x - c)^n dx$

Definite integral from $0$ to $\infty$ of $a_n dx$

Limit as $n$ approaches infinity of $|a_{n+1}/a_n|$

The presence of only linear terms along with constant coefficients allowing straightforward use of usual calculus rules due tractability factor

A single variable under standard functional forms like polynomials, exponentials, logarithms; trigonometric ratios without any composing other than multiplication / division amongst them would suffice

Every term can be easily integrated individually without requiring special techniques such as parts-by-parts substitution, thus enabling the cumulative process to take place smoothly across the full spectrum of individual elements concerned here herein

Power series representations must exist for all components within the integrand's expression over some interval around point c in its domain

$R=2$

$R=4$

$R=1$

$R=\infty$

Scale by a nonzero constant

Reflection across an axis

Translation along the x-axis

Rotation about an axis

$\frac{3}{5}, \frac{8}{5}$

$(-4, -2)$

$[-4, -2]$

$(-\frac{8}{5}, -\frac{6}{5})$

(-2, 2]

(-2, 2)

(-1/2, 1/2)

[-1/2, 1/2]

[1,3]

(1,3)

(2, ∞)

(0, 4)

(0, 3)

$( \frac{-1}{3}, \frac{1}{3} )$

[0, \infty)

$(-\infty, \infty)$

It changes only the interval but not the radius.

It changes only the radius but not the interval.

It does not change either attribute.

It changes both attributes.

Pointwise convergent

Conditionally convergent

Absolutely convergent

Uniformly convergent