a.
b.
c.

To solve these limits, we’ll use algebraic simplifications and L’Hôpital’s Rule where necessary.

a. For , we can directly substitute into the expression. The numerator becomes and the denominator becomes . So, we have the indeterminate form . Applying L’Hôpital’s Rule, we differentiate the numerator and denominator:

Now substituting ,

b. For , substituting gives us , which is again indeterminate. Applying L’Hôpital’s Rule results in:

Now substituting ,

c. For , substituting gives . We apply rationalization to get rid of the square roots:

Multiply numerator and denominator by :

Now we can directly substitute :

If we simplify further using L’Hôpital’s Rule again, resulting in:

Continuing through derivatives will yield that

So, the final results are:

a.

b.

c.