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Evaluate the below given limit.
Solution
Note as well that we actually do have to do the right-hand limit here. We know that the natural logarithm is just described for positive x and thus it is the only limit that makes any sense.
Now, in the limit, we obtain the indeterminate form (0) (-∞). L'Hospital's Rule won't apply on products, it works on quotients only. Though, we can turn it into a fraction if we rewrite things a little.
The function is the similar, just rewritten, & now the limit is in the form -∞ /∞ and now we can utilizes L'Hospital's Rule.
Now, it is a mess, however it cleans up nicely.
Now let's take a look at the indeterminate forms,
1^{∞} 0^{0} ∞^{0}
These can all be dealt with in the given way therefore we'll just work one example.
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