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 if a limit does not exist (DNE)?

Back

It means that 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

You can substitute the value into the function, unless it results in an indeterminate form.

Front

What is an indeterminate form?

Back

An indeterminate form is an expression that does not have a well-defined limit, such as 0/0 or ∞/∞.

Front

What is the limit of f(x) = 3x + 2 as x approaches 1?

Back

The limit is 5.

Front

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

Back

The limit is 4.

Front

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

Back

The limit is +∞.

Front

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

Back

The limit is -∞.

Front

What is the Squeeze Theorem?

Back

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