find lim x→2 f(x).

Question

If 2x − 1 ≤ f(x) ≤ x² − 2x + 3 for x ≥ 0, find lim x→2 f(x).

Answer 1

2x - 1 ≤ f(x) ≤ x² - 2x + 3

So, lim_x→2 (2x - 1) ≤ lim_x→2 f(x) ≤ lim_x→2 (x² - 2x + 3)

(2(2)-1) ≤ lim_x→2 f(x) ≤ (2² - 2(2) + 3)

3 ≤ lim_x→2 f(x) ≤ 3

By the Squeeze Theorem, lim_x→2 f(x) = 3.