Limits from a graph

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 a graph?

Back

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

Front

What does it mean if a limit does not exist?

Back

It means that the function does not approach a specific value as the input approaches a certain point.

Front

What is the limit of f(x) as x approaches -2 if f(-2) is defined as 0?

Back

The limit of f(x) as x approaches -2 is 0.

Front

What is the limit of f(x) as x approaches 0 if f(0) is defined as 3?

Back

The limit of f(x) as x approaches 0 is 3.

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

What does it mean for a function to be continuous at a point?

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

How can you identify vertical asymptotes from a graph?

Back

Vertical asymptotes can be identified where the function approaches infinity or negative infinity as x approaches a certain value.