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 specific 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 is the limit of a function as x approaches a from the right?

Back

It is the value that f(x) approaches as x gets closer to a from values greater than a.

Front

What is the limit of a function as x approaches a from the left?

Back

It is the value that f(x) approaches as x gets closer to a from values less than a.

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

If the limit from the left is 4 and the limit from the right is -2, what can be said about the limit at that point?

Back

The limit does not exist (DNE) because the left-hand limit and right-hand limit are not equal.

Front

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

Back

The limit is 2.

Front

How do you determine the limit graphically?

Back

By observing the behavior of the function's graph as it approaches a specific x-value from both sides.

Front

What is a one-sided limit?

Back

A one-sided limit is the limit of a function as the input approaches a specific value from one side only (left or right).