How to Solve Systems that Have More than Two Equations
Larger systems of linear equations involve more than two equations that go along with more than two variables. These larger systems can be written in the form Ax + By + Cz + . . . [more…]
How to Graph a Rational Function When the Numerator Has the Higher Degree
Rational functions where the numerator has the greater degree don’t actually have horizontal asymptotes. Instead, they have oblique asymptotes which you find by using long division. [more…]
How to Graph a Parabola
In order to graph a parabola correctly, it is important to note whether it is a horizontal or a vertical parabola. This is because while the variables and constants in the equations for both curves serve [more…]
How to Measure Angles with Radians
Degrees aren’t the only way to measure angles. You can also use radians. Degrees and radians are just two different ways to measure angles, like inches and centimeters are two ways of measuring length. [more…]
The Riemann Sum Formula For the Definite Integral
The Riemann Sum formula provides a precise definition of the definite integral as the limit of an infinite series. The Riemann Sum formula is as follows [more…]
How to Solve Limits with a Limit Sandwich
When you can't solve a limit by using algebra, try making a limit sandwich. The best way to understand the sandwich, or squeeze, method is by looking at a graph. [more…]
Even-Odd Identities in Trigonometric Functions
All functions, including trig functions, can be described as being even, odd, or neither. Knowing whether a trig function is even or odd can help you simplify an expression. These even-odd identities are [more…]
Completing the Square for Conic Sections
When the equation of a conic section isn't written in its standard form, completing the square is the only way to convert the equation to its standard form. The steps of the process are as follows: [more…]
Finding the Key Parts of All Hyperbolas
A hyperbola is the set of all points in the plane such that the difference of the distances from two fixed points (the foci) is a positive constant. Hyperbolas always come in two parts, and each one is [more…]
Rules for Adding and Subtracting Matrices
To add or subtract matrices, you have to operate on their corresponding elements. In other words, you add or subtract the first row/first column in one matrix to or from the exact same element in another [more…]
Logarithm Basics
Logarithms are simply another way to write exponents. Exponential and logarithmic functions are inverses of each other. For solving and graphing logarithmic functions [more…]
Pre-Calculus Workbook For Dummies Cheat Sheet
Pre-calculus uses the information you know from Algebra I and II and ratchets up the difficulty level to prepare you for calculus. This cheat sheet is designed to help you review key formulas and functions [more…]
The Most Important Derivatives and Antiderivatives to Know
The table below shows you how to differentiate and integrate 18 of the most common functions. As you can see, integration reverses differentiation, returning the function to its original state, up to a [more…]
The Sum Rule, the Constant Multiple Rule, and the Power Rule for Integration
When you perform integration, there are three important rules that you need to know: the Sum Rule, the Constant Multiple Rule, and the Power Rule.
The Sum Rule for Integration tells you that it’s okay to [more…]
How to Solve Compound Functions Where the Inner Function Is ax + b
Some integrals of compound functions f(g(x)) are easy to do quickly in Calculus. These include compound functions for which you know how to integrate the outer function [more…]
Solve Compound Functions Where the Inner Function Is ax
When figuring Calculus problems, some integrals of compound functions f (g(x)) are easy to do quickly. These include compound functions for which you know how to integrate the outer function [more…]
Integration by Parts with the DI-agonal Method
The DI-agonal method is basically integration by parts with a chart that helps you organize information. This method is especially useful when you need to integrate by parts more than once to solve a problem [more…]
How to Solve Integrals with Variable Substitution
In Calculus, you can use variable substitution to evaluate a complex integral. Variable substitution allows you to integrate when the Sum Rule, Constant Multiple Rule, and Power Rule don’t work. [more…]
How to Use Integration by Parts
When doing Calculus, the formula for integration by parts gives you the option to break down the product of two functions to its factors and integrate it in an altered form. To use integration by parts [more…]
Calculus II For Dummies Cheat Sheet
By its nature, Calculus can be intimidating. But you can take some of the fear of studying Calculus away by understanding its basic principles, such as derivatives and antiderivatives, integration, and [more…]
Understanding Infinite Series in Calculus
In calculus, an infinite series is "simply" the adding up of all the terms in an infinite sequence. Despite the fact that you add up an infinite number of terms, some of these series total up to an ordinary [more…]
Evaluating Limits in Calculus
The mathematics of limits underlies all of calculus. Limits sort of enable you to zoom in on the graph of a curve — further and further — until it becomes straight. Once it's straight, you can analyze [more…]
Calculus: How to Solve Differentiation Problems
In calculus, the way you solve a derivative problem depends on what form the problem takes. Common problem types include the chain rule; optimization; position, velocity, and acceleration; and related [more…]
Calculus: Techniques of Integration
You'll find that there are many ways to solve an integration problem in calculus. The following list contains some handy points to remember when using different integration techniques: [more…]
Solving Integration Problems in Calculus
Calculus riddle: What do the Mean Value Theorem, the Washer and Shell Methods, and the Arc Length and Surface of Revolution formulas have in common? They all involve integration. Integration is very fancy [more…]
