Trigonometric limit problems revolve around three formulas, so it’s critical that we know these trig limit formulas. When we solve trigonometric limit problems, our goal is always to reduce the function to a combination of nothing but these three formulas and simple constants.
Read MoreConjugate method can only be used when either the numerator or denominator contains exactly two terms. In order to use it, we have to multiply by the conjugate of whichever part of the fraction contains the radical. The conjugate of two terms is those same two terms with the opposite sign in between them. Notice that we multiply both the numerator and denominator by the conjugate, because that’s like multiplying by 1, which doesn’t change the value of the original function.
Read MoreAs we’ve seen in previous lessons, the simplest way to evaluate a limit is to substitute the value we’re approaching into the function. Because it’s the easiest and fastest method, we should always try substitution first. But substitution won’t always work.
Read MoreThere’s a difference between “limits at infinity” and “infinite limits.” When we see limits at infinity, it means we’re talking about the limit of the function as we approach infinity or negative infinity. Contrast that with infinite limits, which means that the value of the limit is infinity or negative infinity as we approach a particular point.
Read MoreThe intermediate value theorem is a theorem we use to prove that a function has a root inside a particular interval. The root of a function, graphically, is a point where the graph of the function crosses the x-axis. Algebraically, the root of a function is the point where the function’s value is equal to 0.
Read MoreYou should have some intuition about what it means for a graph to be continuous. Basically, a function is continuous if there are no holes, breaks, jumps, fractures, broken bones, etc. in its graph. You can also think about it this way: A function is continuous if you can draw the entire thing without picking up your pencil. Let’s take some time to classify the most common types of discontinuity.
Read MoreL’Hospital’s Rule is used to get you out of sticky situations with indeterminate limit forms. If you plug in the number you’re approaching to the function for which you’re trying to find the limit and your result is one of the indeterminate forms above, you should try applying L’Hospital’s Rule.
Read MoreIf you tried to solve the limit with substitution and it didn’t work, factoring should be the next thing you try. The goal will be to factor the function, and then cancel any removable discontinuities, in order to simplify the function, so that it can be evaluated.
Read MoreWhen you hear your professor talking about limits, he or she is usually talking about the general limit.
Read MoreRemember 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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