AP Calculus Ch. 9 Vocab

Absolute Value Theorem

Consider the sequence {a_n}. If lim n→∞ |a_n| = 0, then lim n→ a_n = 0

Arithmetic Sequence

A sequence that can be written in the form {a, a+d, a+2d, …, (n-1)d,…} for some common difference d

Converge Sequence

A sequence converges if it has a limit

Diverge Sequence

An infinite sequence that has no limit as n→∞

Explicit Sequence

A sequence is defined explicitly when a_n is an equation in terms of n

Finite Sequence

A sequence whose domain has a finite number of elements

Geometric Sequence

A sequence of the form a, ar, ar²,…, arⁿ,…, in which each term after the first term is obtained by multiplying its preceding term by the same number r. The number r is the common ratio of the sequence.

Improper Integral

An integral on an infinite interval or on a finite interval containing one or more points of infinite discontinuity of the integrand. Its value is found as a limit or sum of limits.

L'Hôpital's Rule

Limit of a Sequence

Recursive Sequence

A sequence is defined recursively when a_n is given in terms of the sequence

Sandwich Theorem for Sequences

If lim n→∞ a_n = lim n→∞ c_n = L and if there is an integer N for which a_n≤b_n≤c_n for all n>N, then lim n→∞ b_n = L

Transitivity of Growing Rates

If f grows a the same rate as g as x→∞ and g grows at the same rate as h as x→∞, then f grows at the same rate as h as x→∞