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
Scientific notation - How to do it?

Scientific notation is all about proper form. There’s only format that qualifies as proper scientific notation, and that’s the product of a decimal term and a power of 10. Moreover, the number to the left of the decimal point must be between 1 and 9.

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Krista King
Euler’s method - How to use it?

Euler’s method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can’t be solved using a more traditional method, like the methods we use to solve separable, exact, or linear differential equations.

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Krista King