evaluate the following limits. if needed, enter inf for ∞ and -inf for - (a) lim (22x² + 24x³) = x→∞ (b) lim…

Explanation:

Step1: Identify dominant - term

For a polynomial function (f(x)=22x^{2}+24x^{3}), as (x\to\pm\infty), the term with the highest degree dominates. The highest - degree term is (24x^{3}).

Step2: Evaluate limit as (x\to\infty)

When (x\to\infty), we consider the sign of the leading - term. Since the coefficient of (x^{3}) is positive ((a = 24>0)) and the power of (x) is odd, (\lim_{x\to\infty}(22x^{2}+24x^{3})=\lim_{x\to\infty}24x^{3}=\text{INF}).

Step3: Evaluate limit as (x\to-\infty)

When (x\to-\infty), for the term (24x^{3}), since the power of (x) is odd and the coefficient (a = 24>0), (\lim_{x\to-\infty}(22x^{2}+24x^{3})=\lim_{x\to-\infty}24x^{3}=-\text{INF}).

Answer:

(a) INF (b) -INF