<u><em>No, if the left-hand limit fo a function approaches infinity because there is a vertical aymptote the limit does not exist.</em></u>
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Explanation:
<h2>Important: infinity is not a value!</h2>
When it is said that a limit approaches infinity, it means that the function becomes indefinitely large: as you get closer and closer to the input value, the function becomes larger and larger; in this case, no value can be assigned to the limit, that is, <em>the limit does not exist</em>
For there to be a limit, the function has to approach a specific value. Infinity is not a number; it does not indicate a particular value; again, the limit does not exist.