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 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 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.
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