I wouldn't be surprised if the book is wrong, considering that they can't even use latex correctly.
You have the correct answer.
The question is either absurd or incomplete (see below) because as posted there is no way of knowing .
eg. If , and then it should be clear that . However:
where A and B and hence C and D are completely arbitrary.
The missing information is most likely the fact that either OR . In which case it should be clear from l'Hopital's rule that the answer would indeed be 3/4.
Perhaps you should discuss all this with your professor who "seems to always be right" ....