Special Trig Limits and Continuity

Front

What is a jump discontinuity?

Back

A jump discontinuity occurs when the left-hand limit and right-hand limit of a function at a certain point exist but are not equal. This results in a 'jump' in the graph of the function.

Front

Define left-hand limit.

Back

The left-hand limit of a function at a point is the value that the function approaches as the input approaches that point from the left side.

Front

Define right-hand limit.

Back

The right-hand limit of a function at a point is the value that the function approaches as the input approaches that point from the right side.

Front

What does it mean if a limit is undefined?

Back

A limit is undefined if the function does not approach a specific value as the input approaches a certain point, often due to discontinuities or oscillations.

Front

What is the limit notation for approaching from the left?

Back

Front

What is the limit notation for approaching from the right?

Back

Front

Back

A jump discontinuity at x = 1.

Front

What is the significance of a removable discontinuity?

Back

A removable discontinuity occurs when a function is not defined at a point, but the limit exists. It can often be 'fixed' by redefining the function at that point.

Front

Back

The function approaches the value 4 as x approaches 0.

Front

Back

The function approaches the value -1 as x approaches -4 from the right.