I wouldn't be surprised if the book is wrong, considering that they can't even use latex correctly.
You have the correct answer.
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" ....