As can be seen from the left most limit, we have 4. The right one is 1/2.
And the limit is 2.
We haven't covered l'Hospital's rule yet so Wolfram Alpha's not all that helpful, and even if I did know it it wouldn't have flown on the exam.
I had misread it as cosine squared x, and that is in fact how I solved it on the test which I got no credit for, for some reason.