Sequences and Functions S2

Maximum and Minimum of a Set

Upper and Lower Bounds of a Set, Boundedness

Supremum and Infimum of a Set

Archimedean Postulate

Triangle Inequality (and Reverse)

Bounded Above and Below Further Definition

Convergence of a Sequence

Boundedness of a Sequence

Divergence to ±infinity

Monotone sequence descriptions

Sandwich Theorem

Monotone Convergence Theorem

Subsequences

Bolzano-Weierstrass Theorem

Infinite Series and Partial Sum

Series Convergence

Absolute Convergence of Series

Comparison Test

Ratio Test

MODULUS

Leibniz’s Alternating Series Test

Power Series

Notice how these series start n=0

Radius of Convergence

Ratio Test and Radius of Convergence

Exponential Function

Multiplication of Exponential Function

Trigonometric Functions

Cluster Point

Limit of a Function

Function Converging to Limit

Function Diverging

Continuity

Intermediate Value Theorem

Natural Logarithm

Powers

Maximum/Minimum Point

Weierstrass Extreme value theorem

Interior Point

Derivatives

Local Maximum/Minimum Point

Monotone Functions

L’Hopital’s Rule

Useful Series to Know