To find the limit , let’s simplify the expression inside the limit first.

As approaches infinity, we can simplify:

Taking the limit as approaches infinity, we find:

Thus,

Now our limit has transformed to:

However, this limit can be deceptive in indicating indeterminate forms, if expressed differently, so we need to investigate further using the exponential form. Rewrite:

Now simplify :

As , we can use the approximation :

Then,

As , this approaches:

Finally, substituting this back into the exponent:

Thus, the final limit is: