TEST Limits Graphically/Numerically

Front

Does f(a) have to be defined as we take the limit of f(x) as x approaches 'a'?

Back

No, f(a) does not need to be defined for the limit to exist.

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 limit to exist?

Back

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

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 difference between a one-sided limit and a two-sided limit?

Back

A one-sided limit considers the approach from one side (left or right), while a two-sided limit considers both sides.

Front

What is the left-hand limit?

Back

The left-hand limit is the value that f(x) approaches as x approaches a from the left, denoted as lim (x -> a-) f(x).

Front

What is the right-hand limit?

Back

The right-hand limit is the value that f(x) approaches as x approaches a from the right, denoted as lim (x -> a+) f(x).

Front

What does it mean if the left-hand limit and right-hand limit are not equal?

Back

If they are not equal, the two-sided limit does not exist.

Front

Can a limit exist if the function is not defined at that point?

Back

Yes, a limit can exist even if the function is not defined at that point.

Front

What is a removable discontinuity?

Back

A removable discontinuity occurs when a limit exists at a point, but the function is not defined there.