Find the value for the constant so that

is finite and is not equal to zero. Compute the value of the limit.

We know from the previous exercise that

To apply this result, we first make the substitution , then as and we have

Now, since as we can apply the result of the previous exercise we stated above which tells us

Therefore,

Now, for this limit to be finite and non-zero we need the term in the numerator to have no constant terms (otherwise the in the denominator will make the limit infinite). So, we need which means or . Substituting this value of we then evaluate the limit