This question, apparently from an online mathematics course, is clearly a mistake, which should have been corrected before releasing it to students.
I suggest that the cosine argument should have been:
(1) x/(x²+10) + 3π/2 or perhaps (2) x/(x²+10) + x³/2.
x/(x²+10)→0 as x→±∞ so the limit would be:
(1) 0, option c or (2) “does not exist”, option d.