Question

Functions as X approaches plus or minus infinity

Compute limx→∞cos(x/x^2+10+√3/2).

Answer 1

As described in the image, none of the option is correct.

The answer should be

cos(sqrt(3)/2) or 0.6478593

Answer 2

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.