Limits and Continuity

Front

What is a limit in calculus?

Back

A limit is a value that a function approaches as the input approaches some value.

Front

Define continuity at a point.

Back

A function is 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 removable discontinuity?

Back

A removable discontinuity occurs when a function is not defined at a point, but can be made continuous by defining or redefining the function at that point.

Front

What is a jump discontinuity?

Back

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

Front

What does it mean for a function to be discontinuous?

Back

A function is discontinuous at a point if it is not continuous at that point, meaning either the limit does not exist or does not equal the function's value.

Front

How do you find the limit of a quotient of two functions?

Back

Front

What is the definition of a continuous function?

Back

A function is continuous on an interval if it is continuous at every point in that interval.

Front

Back

It represents the value that f(x) approaches as x approaches c.

Front

What is an essential discontinuity?

Back

An essential discontinuity occurs when the limit does not exist due to oscillation or unbounded behavior.

Front

How can you determine if a function is continuous at a specific point?

Back

Check if the limit exists at that point, and if it equals the function's value at that point.