Limits from Graphs

Front

What is a limit in calculus?

Back

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

Front

How do you determine the limit of a function from its graph?

Back

You observe the y-values that the function approaches as the x-values get closer to a specific point.

Front

What does it mean if the limit of a function exists?

Back

It means that as the input approaches a certain value, the output approaches a specific number.

Front

What is the difference between a limit and the actual value of a function at a point?

Back

A limit describes the behavior of a function as it approaches a point, while the actual value is the function's output at that point.

Front

What does it indicate if the limit of a function does not equal the function's output?

Back

It indicates that the function may have a discontinuity at that point.

Front

What is a removable discontinuity?

Back

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

Front

What is an infinite limit?

Back

An infinite limit occurs when the function increases or decreases without bound as the input approaches a certain value.

Front

How can you identify vertical asymptotes using limits?

Back

Vertical asymptotes can be identified where the limit of a function approaches infinity as the input approaches a certain value.

Front

What is the Squeeze Theorem?

Back

The Squeeze Theorem states that if a function is squeezed between two other functions that have the same limit at a point, then the squeezed function also has that limit.