Limits Graphically

Front

What is a limit in calculus?

Back

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

Front

What does it mean for a limit to exist?

Back

A limit exists if the function approaches the same value from both the left and right sides as x approaches a certain point.

Front

What is the notation for the limit of f(x) as x approaches a?

Back

The notation is lim (x -> a) f(x).

Front

What does 'approaching from the left' mean?

Back

It means considering values of x that are less than a, approaching a from the left side.

Front

What does 'approaching from the right' mean?

Back

It means considering values of x that are greater than a, approaching a from the right side.

Front

What is the limit of f(x) as x approaches -4 from the left if f(x) = 2?

Back

The limit is 2.

Front

What is the limit of f(x) as x approaches 1 from the left if f(x) = 4?

Back

The limit is 4.

Front

What is the limit of f(x) as x approaches 1 from the right if f(x) = -2?

Back

The limit is -2.

Front

What does DNE stand for in limits?

Back

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

Front

How can you determine if a limit is DNE?

Back

A limit is DNE if the left-hand limit and right-hand limit do not equal each other or if the function approaches infinity.