Calculus Limits and Continuity

Front

What is a limit in calculus?

Back

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

Front

What does it mean for a limit to exist?

Back

For a limit to exist, the left-hand limit and the right-hand limit must be equal.

Front

What is the limit of f(x) as x approaches 1 from the right if f(x) = -2?

Back

-2

Front

What is the limit of f(x) as x approaches -2 if it does not exist?

Back

DNE (Does Not Exist)

Front

What is continuity in calculus?

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

Back

2

Front

What is the notation for limits?

Back

The notation for limits is lim, followed by the variable and the value it approaches, e.g., lim (x -> a) f(x).

Front

What is the difference between one-sided limits and two-sided limits?

Back

One-sided limits consider the approach from one direction (left or right), while two-sided limits consider both directions.

Front

What does DNE stand for in the context of limits?

Back

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

Front

What is the limit of a constant function?

Back

The limit of a constant function as x approaches any value is the constant itself.