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Mastering Monotonic and Bounded Sequences in Mathematics

Analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies

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Evaluating piecewise functions

Graphing piecewise linear functions

Graphing piecewise non-linear functions

Difference quotient: applications of functions

Solve problems that involve the application of set theory

Set notation

Understanding How to Use Set Notation

Set builder notation

Intersection and union of 2 sets

Intersection and Union of 2 Sets

Intersection and union of 3 sets

Intersection and Union of 3 Sets

Solve problems that involve conditional statements

Inverse functions

Probability with Venn diagrams

Interpret and assess the validity of odds and probability statements

Continuous growth and decay

Addition rule for 

Addition Rule for "OR"

Addition rule for "OR"

Multiplication rule for 

Multiplication rule for "AND"

Multiplication Rule for "AND"

Solve problems that involve the probability of mutually exclusive and non-mutually exclusive events

Conditional probability

Probability involving permutations and combinations

Solve problems that involve the probability of two events

Law of total probability

Law of Total Probability

Probability of a randomly selected employee meeting a sales target

Probability of a randomly selected driver being involved in an accident

Probability of a randomly selected customer making a purchase

Probability of a randomly selected person being overweight

Bayes' rule

Bayes" Rule

Bayes rule

Bayes" rule

Bayes' Rule

Solve problems that involve the fundamental counting principle

Fundamental counting principle

Fundamental Counting Principle Involving Restrictions

Factorial notation

Path counting problems

Introduction to sequences

Monotonic and bounded sequences

Solve problems that involve permutations

Permutations

Permutation vs. Combination

Solve problems that involve combinations

Combinations

Problems involving both permutations and combinations

Expand powers of a binomial using the binomial theorem

Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

Binomial theorem

Represent data, using polynomial functions (of degree ≤ 3), to solve problems

Polynomial long division

Polynomial synthetic division

Polynomial functions

Recognizing a Polynomial Function

Remainder theorem

Finding the Remainder Using Synthetic Division and the Remainder Theorem

Factor theorem

Using the Factor Theorem to Test For Factors of a Polynomial

Rational zero theorem

Rational Zero Theorem

Characteristics of polynomial graphs

Determining the equation of a polynomial function

Applications of polynomial functions

Multiplicities of polynomials

Imaginary zeros of polynomials

Solving polynomial inequalities

Represent data, using exponential and logarithmic functions, to solve problems

Solving logarithmic equations

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

What is a logarithm?

Logarithms and Exponential Growth

Understanding Logarithms through Exponential Growth

Understanding Logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Graphing logarithmic functions

Exponential growth and decay by a factor

Exponential decay: Half-life

Finance: Compound interest

Finance: Compound Interest

Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: pH scale

Represent data, using sinusoidal functions, to solve problems

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Cotangent graph: y = cot x

Secant graph: y = sec x

Cosecant graph: y = csc x

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

Demonstrate an understanding of normal distribution, including standard deviation and z-scores

Spread of a data set - standard deviation & variance

Measures of relative standing - z-score, quartiles, percentiles

Introduction to normal distribution

The Normal Distribution and the 68-95-99.7 Rule

Using "invNorm" to Solve Normal Distribution Problems

Normal distribution and continuous random variable

Z-scores and random continuous variables

Sampling distributions

Understanding Proportions and Sample Size

Central limit theorem

Central Limit Theorem

Applying the Central Limit Theorem

Rare event rule

The Rare Event Rule for the Central Limit Theorem

Interpret statistical data, using confidence intervals, confidence levels, margin of error

Point estimates

Confidence levels and critical values

Margin of error

Margin of Error

Making a confidence interval

Chi-Squared confidence intervals

Chi-Squared Confidence Intervals

Confidence intervals to estimate population mean

Student's t-distribution

Student"s t-distribution

Determining a Confidence Interval for a Population Mean using t-distributions

Foundations of Mathematics 120

Logical Reasoning

Probability

Relations and Functions

math

Intro

Ex.1

Ex.2

Ex.3

In this section, we will be talking about monotonic and bounded sequences. We will learn that monotonic sequences are sequences which constantly increase or constantly decrease. We also learn that a sequence is bounded above if the sequence has a maximum value, and is bounded below if the sequence has a minimum value. Of course, sequences can be both bounded above and below. Lastly, we will take a look at applying theorem 7, which will help us determine if the sequence is convergent. One important to note from the theorem is that even if theorem 7 does not apply to the sequence, there is a possibility that the sequence is convergent. It's just that the theorem will not be able to show it.

What are monotonic and bounded sequences?