Summative One-sided Limits 8th block

Front

What is a one-sided limit?

Back

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

Front

What does \( \lim_{x \to a^-} f(x) \) represent?

Back

It represents the left-hand limit of the function \( f(x) \) as \( x \) approaches \( a \) from the left.

Front

What does \( \lim_{x \to a^+} f(x) \) represent?

Back

It represents the right-hand limit of the function \( f(x) \) as \( x \) approaches \( a \) from the right.

Front

How do you determine the right-hand limit from a graph?

Back

To determine the right-hand limit, observe the value that the function approaches as you move towards the point from the right side.

Front

How do you determine the left-hand limit from a graph?

Back

To determine the left-hand limit, observe the value that the function approaches as you move towards the point from the left side.

Front

What is the limit of a function if both one-sided limits are equal?

Back

If both the left-hand limit and right-hand limit are equal, then the limit exists and is equal to that common value.

Front

What is the limit of a function if the left-hand limit is not equal to the right-hand limit?

Back

If the left-hand limit and right-hand limit are not equal, then the limit does not exist (DNE).

Front

What is the limit of the function as \( x \) approaches 2 from the right if the function value is 5?

Back

The limit is 5.

Front

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

Back

The limit is 2.

Front

What does DNE stand for in limit notation?

Back

DNE stands for 'Does Not Exist', indicating that the limit cannot be determined.