Find values for the constants and so that

First, since the integral is continuous (Theorem 3.4 of Apostol) we know

We also have

Hence, we may apply L’Hopital’s rule to the quotient giving us (using the First Fundamental Theorem of Calculus for the numerator)

Since the limit as of the numerator is 0, we must have the limit of the denominator equal to 0 as well (otherwise the whole limit would be 0 instead of 1).

Now, substituting back into our limit and using L’Hopital’s two more times (since again we have the indeterminate form ),

Therefore,

Hence, the requested constants are