Negative exponents

Remember that any number can be written as itself divided by 1. For example, 3 is the same as 3/1. Also remember that the top part of a fraction is called the numerator and the bottom part of a fraction is called the denominator.

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Krista King
Sketching direction fields

What you want to do is create a field of equally spaced coordinate points, and then evaluate the derivative at each of those coordinate points. Since the derivative is the same thing as the slope of the tangent line, finding the derivative at a particular point is like finding the slope of the tangent line there, which of course is an approximation of the slope of the actual function.

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Krista King
Plotting points in three dimensions

In the same way that we plot points in two-dimensional coordinate space by moving out along the x-axis to our x value, and then moving parallel to the y-axis until we find our point, in three-dimensional space we’ll move along the x-axis, then parallel to the y-axis, then parallel to the z-axis until we arrive at our coordinate point.

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Krista King
Zero as an exponent

Any nonzero real number raised to the power of zero is one, this means anything that looks like a^ will always equal 1 if "a" is not equal to zero.

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Krista King
Commutative property

Commutative comes from the word “commute” as in “the morning commute.” Since commute means to move you can remember that, when using the commutative property, the numbers will move around.

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Krista King
Limits of composite functions - How to find them?

Remember that composite functions are “functions of functions”, which means that we have one function plugged into another function. As an example, sin(x^2) is a composite function because we’ve plugged the function x^2 into the function sin(x). Think of any function that as an “outer part” and an “inner part” as composite functions.

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Krista King
Error bounds

Remember that midpoint rule, trapezoidal rule, and Simpson’s rule are all different ways to come up with an approximation for area under the curve.

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Krista King