Continuity

Front

What is continuity in mathematics?

Back

Continuity refers to a function being continuous at a point if the limit of the function as it approaches that point equals the function's value at that point.

Front

What is a continuous function?

Back

A function is continuous if, for every point in its domain, the limit of the function as it approaches that point equals the function's value at that point.

Front

Define removable discontinuity.

Back

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

Front

What is infinite discontinuity?

Back

Infinite discontinuity occurs when the function approaches infinity as it approaches a certain point from either side.

Front

What is jump discontinuity?

Back

Jump discontinuity occurs when the left-hand limit and right-hand limit at a point exist but are not equal.

Front

How do you determine if a function is continuous at a point x = a?

Back

A function f(x) is continuous at x = a if: 1) f(a) is defined, 2) the limit as x approaches a exists, and 3) the limit equals f(a).

Front

What does it mean if a function has a limit that does not equal the function's value at a point?

Back

It indicates that the function has a discontinuity at that point.

Front

What is the limit notation for approaching a point from the left?

Back

Front

What is the limit notation for approaching a point from the right?

Back

Front

What is the condition for a function to have a removable discontinuity at x = a?

Back