Use the Squeeze Theorem to evaluate the limit lim x→10 f(x), if −1x + 110 ≤ f(x) ≤ x^2 on [8,12].

Question

Use the Squeeze Theorem to evaluate the limit lim _x→10 f(x), if −1x + 110 ≤ f(x) ≤ x^2 on [8,12].

Answer 1

Evaluate the limit as x → 10 of the outer functions: lim(-x + 110) = -10 + 110 = 100 and lim(x²) = 10² = 100. Since these limits are both 100 and -x + 100 ≤ f(x) ≤ x² on [8, 12], by the squeeze theorem, the limit of f(x) as x → 10 is 100.