determine whether the limit is equal to ∞ or -∞. \nlim(x→∞) x² - 6\n\nchoose the correct answer…

Explanation:

Step1: Analyze the function as x approaches infinity

As (x\to\infty), the term (x^{2}) dominates the function (y = x^{2}-6). Since (x^{2}) is a quadratic function with a positive leading - coefficient ((a = 1>0)), when (x) gets larger and larger, (x^{2}) also gets larger and larger. The value of (x^{2}) goes to infinity as (x\to\infty), and subtracting 6 from a very large positive number still results in a very large positive number.

Step2: Determine the limit

We have (\lim_{x\to\infty}(x^{2}-6)=\lim_{x\to\infty}x^{2}-\lim_{x\to\infty}6). Since (\lim_{x\to\infty}x^{2}=\infty) and (\lim_{x\to\infty}6 = 6), then (\lim_{x\to\infty}(x^{2}-6)=\infty).

Answer:

(\lim_{x\to\infty}x^{2}-6=\infty)