Question

Please help! A, B, C, D, or E?

Answer 1

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.

$\lim_{x \to -3^+} g(x) = - \infty$

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.

$\lim_{x \to \infty} \frac{x+ c}{x+3} = \frac{x}{x} = 1$

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