Limits

Front

What is the limit?

Back

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

Front

What does it mean for a function to be continuous?

Back

A function is continuous if the limit as x approaches a point equals the function's value at that point.

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.

Front

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

Back

The limit as x approaches infinity can be a finite number, infinity, or DNE (does not exist) depending on the function.

Front

What is the Squeeze Theorem?

Back

The Squeeze Theorem states that if f(x) ≤ g(x) ≤ h(x) for all x in some interval and the limits of f and h are equal at a point, then the limit of g at that point is also equal to that limit.

Front

What is a one-sided limit?

Back

A one-sided limit is the value that a function approaches as the input approaches a certain point from one side (left or right).

Front

What is the limit of (x^2 - 1)/(x - 1) as x approaches 1?

Back

The limit is 2, found by factoring and simplifying the expression.

Front

What is the limit of sin(x)/x as x approaches 0?

Back

The limit is 1.

Front

What is the difference between a limit and a value?

Back

A limit is the value a function approaches, while a value is the actual output of the function at a specific input.

Front

What is L'Hôpital's Rule?

Back

L'Hôpital's Rule is a method for finding limits of indeterminate forms by differentiating the numerator and denominator.