36 x − 2 x 2 − 153 < g ( x ) < x 2 − 18 x + 90

Question

Suppose the function g statisfies 

36x−2x^2−153< g(x) < x^2−18x+90

We want to use the Squeeze Theorem to evaluate limx→9 g(x)

1. First evaluate:  limx→9 36x−2x^2−153
2. Next evaluate:  limx→9. x^2−18x+90

Therefore, by the Squeeze Theorem, limx→9. g(x)=

Answer 1

Yes, your outline is correct. Observe that

lim x -> 9 (36x - 2x^2 -153) = 36 * 9 - 2 * 9**2 - 153 = 9

and

lim x->9 (x^2 - 18x + 90) = 81 - 18 * 9 + 90 = 9.

Thus by the squeeze theorem, lim x->9 g(x) = 9.