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 DNE stand for in limits?

Back

DNE stands for 'Does Not Exist', indicating that a limit does not approach a finite value.

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 evaluate limits algebraically?

Back

To evaluate limits algebraically, substitute the value into the function, and simplify if necessary.

Front

What is the limit of (x^2 - 4)/(x - 2) as x approaches 2?

Back

The limit is 4, after factoring and canceling the common term.

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.

Front

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

Back

The limit is 1.

Front

What is an infinite limit?

Back

An infinite limit occurs when the function increases or decreases without bound as the input approaches a certain value.

Front

What is the limit of (1/x) as x approaches infinity?

Back

The limit is 0.

Front

What is a one-sided limit?

Back

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