Limits for Precalculus

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 be DNE (Does Not Exist)?

Back

A limit is said to DNE if the function does not approach a specific value as the input approaches a certain 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

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

Back

To find the limit, substitute the value into the function, unless it results in an indeterminate form.

Front

What is the limit of f(x) = 3x + 2 as x approaches 4?

Back

The limit is 14.

Front

What is the limit of f(x) = 1/x as x approaches 0 from the right?

Back

The limit is Infinity.

Front

What is the limit of f(x) = 1/x as x approaches 0 from the left?

Back

The limit is -Infinity.

Front

What is the Squeeze Theorem?

Back

The Squeeze Theorem states that if f(x) ≤ g(x) ≤ h(x) for all x near a, and the limits of f and h as x approaches a are equal, then the limit of g as x approaches a is also equal to that limit.

Front

What is the limit of f(x) = x^2 as x approaches 3?

Back

The limit is 9.

Front

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

Back

The limit is 1.