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

How do you find the limit as x approaches a specific value?

Back

Evaluate the function at values increasingly close to that specific value from both sides.

Front

What does it mean if a limit is DNE (Does Not Exist)?

Back

It means that the function does not approach a specific value as x approaches the limit.

Front

What is the limit of f(x) as x approaches 3 if f(x) = 4 when x is near 3?

Back

4

Front

What is the limit of f(x) as x approaches -4 from the left if f(x) = 2 when x is near -4?

Back

2

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity.

Front

How do you find vertical asymptotes of a function?

Back

Set the denominator of the function equal to zero and solve for x.

Front

What is the limit of f(x) as x approaches infinity if f(x) = 20?

Back

20

Front

What is the limit of f(x) as x approaches a value if f(x) approaches infinity?

Back

The limit is infinity.

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.