The dominant term is in the denominator.
As x→∞, the fraction gets closer to 0.
The dominant term is |x| in the numerator (square root of x2 is |x|) and x in the denominator, so the answer is the ratio of the coefficients.
The cosine function oscillates between 1 and −1 forever. Since a limit must approach a single height, the limit does not exist.
Is the graph approaching the SAME height from both sides?
What height is the graph approaching as x→0+?