Limits - Functions

Front

What is a limit in calculus?

Back

A limit is a value that a function approaches as the input approaches some value.

Front

What does it mean for a function to have a hole?

Back

A hole in a function occurs at a point where the function is not defined, typically due to a factor that cancels out in a rational function.

Front

How do you find the x-coordinate of a hole in a rational function?

Back

Set the denominator equal to zero and solve for x, then check if the numerator also equals zero at that x value.

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or crosses.

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes occur where the denominator is zero and the numerator is not zero.

Front

How do you find horizontal asymptotes of a rational function?

Back

Horizontal asymptotes are found by comparing the degrees of the numerator and denominator.

Front

Back

The limit is 3.

Front

What is the limit of a function as x approaches a specific value?

Back

It is the value that the function gets closer to as x gets closer to that specific value.

Front

What does DNE stand for in limits?

Back

DNE stands for 'Does Not Exist', indicating that the limit does not approach a finite value.

Front

Back

The limit is 4.