Question

Suppose that g is a function with -x^2+6x-12  greater than or equal to g(x) less than or equal to x^2-6x+6 for all x.
Evaluate lim
x->3 g(x).

Answer 1

\[\lim_{x \rightarrow 3} g(x)\]
Suppose that g is a function with -x^2+6x-12 <or equal to g(x) <or equal to x^2-6x+6 for all
x.

Answer 2

let the first function be a and the 2nd be b
then
\[-x^2+6x-12 \le g(x) \le x^2-6x+6\]
\[a \le g(x) \le b\]
\[-3^2+6(3)-12 \le g(x) \le 3^2-6(3)+6\]
\[-3 \le g(x) \le -3\]
hence g(x) has to be 3
sandwich theorem