Can anyone me with limits calculus? (qn 32)

I assume you don't know about derivatives yet. The reason I bring that up is because the given limit is equivalent to the derivative of a certain function and you might recognize it later on.

To compute the limit, in the numerator we can combine the fractions into one:

We're taking the limit as , which means we're considering near 0, but not , so that we can simplify:

Then as , we have and , so that

provided that .

(In fact, the limit is equivalent to the derivative of the function , whose derivative is )