**Problem 1:** Evaluate the following limits. When appropriate, declare whether the limit goes to ∞ or -∞ if the limit does not exist.

## Answer

## Explanation

As we learned in the limits article, our first approach when handling limits is to first try evaluating them directly by substituting in the value of the limit for x. In this case, we would substitute 0 for x since the limit is evaluated as x approaches 0.

Therefore, let's plug in 0 for x...

...and solve...

...resulting in 5!

Lucky for us, the direct substitution method worked and gave us our answer! As our function approaches x = 0 from the right and left side, it approaches a y-value of 5!

If we received an indeterminate value like 0/0, then we would've needed to try new techniques.

I’m a Miami University (OH) 2021 alumni who majored in Information Systems. At Miami, I tutored students in Python, SQL, JavaScript, and HTML for 2+ years. I’m a huge fantasy football fan, Marvel nerd, and love hanging out with my friends here in Chicago where I currently reside.