Limits

Front

What is a limit in calculus?

Back

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

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

Define removable discontinuity.

Back

Removable discontinuity occurs when a function is not defined at a point, but the limit exists at that point.

Front

What is infinite discontinuity?

Back

Infinite discontinuity occurs when the function approaches infinity or negative infinity as the input approaches a certain point.

Front

What is a jump discontinuity?

Back

Jump discontinuity occurs when the left-hand limit and right-hand limit at a point are not equal.

Front

What does DNE stand for in limits?

Back

DNE stands for 'Does Not Exist', indicating that a limit cannot be determined.

Front

How do you find the limit as x approaches a number from the right?

Back

To find the limit as x approaches a number from the right, evaluate the function as x gets closer to that number from values greater than it.

Front

How do you find the limit as x approaches a number from the left?

Back

To find the limit as x approaches a number from the left, evaluate the function as x gets closer to that number from values less than it.

Front

What is the limit of a function as x approaches infinity?

Back

The limit of a function as x approaches infinity describes the behavior of the function as x increases without bound.

Front

What does it mean if the limit of a function is infinity?

Back

If the limit of a function is infinity, it means the function increases without bound as x approaches a certain value.