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How do you sketch level curves of multivariable functions?

Whenever you're dealing with a multivariable function, the graph of that function will be a three-dimensional figure in space.

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Learn mathKrista KingSeptember 19, 2017curves, level curves, multivariable functions
One-sided limits

When you hear your professor talking about limits, he or she is usually talking about the general limit.

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Learn mathKrista KingSeptember 7, 2017limits, one-sided limits
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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Learn mathKrista KingSeptember 5, 2017limits, limits of composite functions
Rationalize the denominator

Remember that the phrase “rationalize the denominator” just means “get the square root(s) out of the denominator”.

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Learn mathKrista KingAugust 31, 2017rationalize, denominators
What does a triple integral represent?

It can be difficult to visualize what a triple integral represents, which is why in this video we’ll be answering the question, “What am I finding when I evaluate a triple integral?”

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Learn mathKrista KingAugust 29, 2017triple integral, integrals, trig identities
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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Learn mathKrista KingAugust 24, 2017error bounds
What does a double integral represent?

Trig identities are pretty tough for most people, because 1) there are so many of them, and 2) they’re hard to remember, and 3) it’s tough to recognize when you’re supposed to use them!

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Learn mathKrista KingAugust 22, 2017double integral, integrals, trig identities
Trig identities - What are they?

Trig identities are pretty tough for most people, because 1) there are so many of them, and 2) they’re hard to remember, and 3) it’s tough to recognize when you’re supposed to use them!

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Learn mathKrista KingJuly 11, 2017trig identities
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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Learn mathKrista KingJuly 4, 2017scientific notation
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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Learn mathKrista KingJune 27, 2017euler's method
Graph lines - How to?

The most important thing to remember about graphing lines is that you always need some combination of the slope of the line, and/or points on the line in order to graph it.

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Learn mathKrista KingJune 20, 2017graphing, graph lines
Partial derivatives - How to solve?

Partial derivatives are just like regular derivatives, but for multivariable functions.

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Learn mathKrista KingJune 13, 2017partial derivatives
Pythagorean theorem - What is it?

Pythagorean theorem is a tool you’ll use all the time when you’re dealing with triangles, and you will always be dealing with triangles, no matter what math class you’re taking.

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Learn mathKrista KingJune 6, 2017pythagorean theorem, triangles
Trig substitution - How to solve?

Trigonometric substitution (more affectionately known as trig substitution, or trig sub), is another integration method you can use to simplify integrals. 

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Learn mathKrista KingMay 30, 2017trig substitution, how to solve equations
Exponents - What are they?

Exponents are a fundamental math tool that you learn in Pre-algebra, but a lot of people continue to struggle with them all the way through calculus! ‍‍

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Learn mathKrista KingMay 23, 2017exponents
Graphing polar curves: lemniscates

Graphing polar curves and, more specifically, graphing circles, is a hard thing to master at first. But, with practice, it gets a lot easier, and you'll get much, much faster.

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Learn mathKrista KingMay 8, 2017graphs, graphing polar curves, curves, lemniscates
Two fast ways to multiply by 9

Here are two quick ways to multiply 9 by any number 1 through 10.

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Learn mathKrista KingApril 18, 2017multiplication, multiply by 9, quick multiplication
The 1089 rule (having fun with algebra)

The “1,089 rule” isn’t really a rule at all, it’s more like a fun thing that happens with numbers that you can explain with algebra.

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Learn mathKrista KingApril 3, 20171089 rule, algebra
Area between curves... which curve is which?

When you’re doing an area between curves problem, one of the toughest parts of the problem is figuring out the orientation of the curves.

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Learn mathKrista KingMarch 21, 2017curves, curve
How to add 1 through 100 quickly

If you want to add up all the numbers 1 through anything, like 1 through 100, or 1 through 23, there’s actually an easy way to do it.

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Learn mathKrista KingMarch 13, 2017addition, add 1 through 100, quick addition
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