If $6 x - 1 \leq f ( x ) \leq x ^ { 2 } - 1$,find $\lim _ { x \rightarrow 6 } f ( x )$
A) 1
B) 35
C) 0
D) -6
E) -35

Question

Quizplus · Accepted Answer

We can take the limit as x approaches 6 of both sides of the inequality:
$\lim_{x	o 6}(6x-1)\leq \lim_{x	o 6}f(x)\leq \lim_{x	o 6}(x^2-1)$
$35\leq \lim_{x	o 6}f(x)\leq 35$
Since $\lim_{x	o 6}(6x-1)=35$ and $\lim_{x	o 6}(x^2-1)=35$, the only possible value for the limit of $f(x)$ as $x$ approaches 6 is $\boxed{	extbf{(B) }35}$.

If 6x−1≤f(x)≤x2−16 x - 1 \leq f ( x ) \leq x ^ { 2 } - 16x−1≤f(x)≤x2−1

If $6 x - 1 \leq f ( x ) \leq x ^ { 2 } - 1$