Problem 1a Explanation

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



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.

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