Evaluate the limit using techniques from Chapters 2 and 4 and using L’Hôpital’s Rule.

(a) using techniques from Chapters 2 and 4
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(b) using L’Hôpital’s Rưle

To solve the limit using techniques from Chapters 2 and 4, we first simplify the expression. Notice that the denominator can be factored as . Thus, we rewrite the limit:

Next, we can cancel the terms, provided :

Now substituting :

So, the result is .

Now, applying L’Hôpital’s Rule, we first recognize that substituting results in the indeterminate form . Therefore, we differentiate the numerator and denominator:

Applying L’Hôpital’s Rule gives us:

Substituting :

Thus, using L’Hôpital’s Rule also results in .