The fundamental theorem of calculus (FTC) is the formula that relates the derivative to the integral and provides us with a method for evaluating definite integrals.
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The squeeze theorem allows us to find the limit of a function at a particular point, even when the function is undefined at that point.
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In this lesson we’ll work with both positive and negative fractional exponents.
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Think of an equation as a balance scale that must always be balanced. What you do to one side of an equation you must do to the other in order for it to remain balanced.
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We need to change the current equation so that it's in terms of a new variable u and its derivative u'.
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To find the radius, it’s important that we take the square root of the right-hand side, and not just the full value from the right
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Evaluating a definite integral means finding the area enclosed by the graph of the function and the x-axis, over the given interval [a,b].
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“Limits at infinity” sounds a little mysterious, and it can be difficult to imagine the concept when we first hear this term. But let’s start by remembering that limits can be defined as the restrictions on the continuity of a function.
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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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The distributive property can be used even when there are two sets of parentheses with two terms each. It’s called binomial multiplication (remember that a bicycle has two wheels and a binomial has two terms).
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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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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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Evaluating a definite integral means finding the area enclosed by the graph of the function and the x-axis, over the given interval [a,b].
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When we’re evaluating a limit, we’re looking at the function as it approaches a specific point.
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Simple interest is different than compounded, or compounding, interest. With compounding interest, you earn interest on your interest, so that your money grows exponentially…
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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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In this video we’re talking about jump discontinuities, or discontinuities of the first kind.
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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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When you have multiple functions, you can use some simple rules to find their sum, difference, product, or quotient.
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Keep in mind that present value is the opposite of future value. Future value is how much we need to have at some point in the future; present value is how much we need to have right now.
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