Select the correct choice below and, if necessary, fill in the answer box to complete your
choice.
A.
(Simplify your answer.)
B. The limit does not exist and is neither nor .

When evaluating limits, it’s essential to consider the behavior of the function as it approaches the given value. If is a function defined around and is continuous at that point, then would simply equal . However, if has a removable or jump discontinuity at , the limit might need to be evaluated through one-sided limits or simplification of the function.

In cases where the limit does not exist, it could be due to several reasons such as oscillation or unbounded behavior. For example, if oscillates infinitely as it approaches , then you would conclude that the limit does not exist. It’s also essential to check for any common pitfalls, like mistakenly stating limits that approach infinity when they’re just undefined at that point!