Use the Theorem on Limits of Rational Functions to find the limit. If necessary, state that the limit does not exist.

Select the correct choice below and fill in the answer box within your choice.
A. (Simplify your answer.)
B. The limit does not exist.

To find the limit , notice that the numerator can be factored: . Therefore, the expression simplifies to for , which further simplifies to . Now, we can safely substitute :

So, the answer is .

Now to further enhance your knowledge:

By the concept of limits, particularly the Squeeze Theorem, we can understand how functions behave near certain points. When we have a rational function, if you get a form like , factoring and simplifying is often your best bet to find the limit. Always keep an eye out for opportunities to reduce expressions for clearer insights!

For real-world applications, limits aren’t just for calculus problems; they also play a crucial role in fields like physics, especially in understanding instantaneous rates of change, which is essential in everything from calculating velocity to analyzing motion. Essentially, limits help us dissect how things change and ultimately help in predictions, from engineering designs to financial models!