I) This is False, because as you approach -3 from the right, the denominator is positive making g(x) negative, thus the limit is negative infinity.
II) This is True, as x goes to infinity, cos(x) is bounded between -1 and 1 and can be treated as a constant. Therefore the limit is 1.
III) This is False, the intermediate value theorem only applies on intervals where function is continuous. g(x) is not defined at x=-3, which is in the given interval [-4,0]. Therefore g(x) is not continuous and intermediate value theorem does not apply.
Final Answer:
D) only statement II is True
II) This is True, as x goes to infinity, cos(x) is bounded between -1 and 1 and can be treated as a constant. Therefore the limit is 1.
III) This is False, the intermediate value theorem only applies on intervals where function is continuous. g(x) is not defined at x=-3, which is in the given interval [-4,0]. Therefore g(x) is not continuous and intermediate value theorem does not apply.
Final Answer:
D) only statement II is True