AP Calculus AB/BC #1

Jump Discontinuity

Continuous

Removable Discontinuity

Infinite Discontinuity

Removable Discontinuity

Jump Discontinuity

Infinite Discontinuity

Continuous

x^2

x/2

1/x

2x-5

Use the conjugate method, in which you multiply each part of the fraction by a certain number that simplifies the fraction to something that you can evaluate.

You can't determine the limit(s) only given the function, more information is needed.

Use a table, creating a list of x-values from each side of a that get closer and closer to a, and by plugging them into the function, you can get an answer that approximates the limits of both sides.

Use the plugin method, plug in a into the function, and the limit is the answer you get from it.

Factor out the equation until you get pairs of binomials that you can remove holes from, and then evaluate the function.

Use a calculator and evaluate the radical to the nearest tenth, then evaluate the rest of the function.

Use the conjugate method by multiplying the numerator and denominator by a certain number that simplifies the fraction to something you can evaluate without getting an undefined.

Plug it in, it will yield an answer that you can evaluate using multiplication of radicals that produces a whole number answer.

-5/2

infinity

5/2

0

Plug in infinity and approximate a value that would lead to an accurate answer.

Rule out all unneeded constants and smaller terms and evaluate the term(s) with the degree of the equation.

Use the rule of infinites, where the limit of all functions approaching infinity would be infinity.

Divide the two expressions and the result would be the limit.

The slope of the line that represents the secant of the lowest point on the function

The trigonometric secant of the two highest points on a function

Any line between two points on a function

A line that only touches one point on a function

Doesn't exist

The line that touches exactly one point on a function

Any line between two points on a function

The tangent of the lowest point of a function

The backup secant line of a function

Doesn't exist

The line that touches only the lowest point of a function

A line that doesn't go until x = infinity