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

Back

To find the limit, substitute the value into the function, if the function is defined at that point.

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) = x^2 as x approaches 3?

Back

The limit is 9.

Front

What does it mean for a limit to approach Infinity?

Back

It means that as x gets larger (or smaller), the function's value increases without bound.

Front

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

Back

The limit is 2, after factoring and simplifying.

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.