FLASHCARD Discontinuities and Limits

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 a continuous function.

Back

A function is continuous at a point if the limit as x 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 it at that point.

Front

What is an infinite discontinuity?

Back

An infinite discontinuity occurs when the function approaches infinity or negative infinity as the input approaches a certain value.

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

How do you find the interval of continuity for a function?

Back

The interval of continuity is found by identifying where the function is defined and continuous, excluding points of discontinuity.

Front

What does it mean for a function to be constant over an interval?

Back

A function is constant over an interval if it takes the same value for every input within that interval.

Front

What is an increasing interval?

Back

An increasing interval is a range of x-values where the function's output values increase as x increases.

Front

How do you determine the limit from the right at a point?

Back

To find the limit from the right, evaluate the function as x approaches the point from values greater than the point.

Front

What is the notation for limits?

Back