suppose the function $g$ satisfies $-32x - 2x^{2}-137

Question

suppose the function $g$ satisfies $-32x - 2x^{2}-137<g(x)<x^{2}+16x + 55$. we want to use the squeeze theorem to evaluate $lim_{x
ightarrow - 8}g(x)$. first evaluate: $lim_{x
ightarrow - 8}-32x - 2x^{2}-137$. next evaluate: $lim_{x
ightarrow - 8}x^{2}+16x + 55$. therefore, by the squeeze theorem, $lim_{x
ightarrow - 8}g(x)=$

Accepted Answer

# Explanation:
## Step1: Evaluate $\lim_{x
ightarrow - 8}-32x - 2x^{2}-137$
Substitute $x = - 8$ into $-32x - 2x^{2}-137$.
$$
\begin{align*}
&-32\times(-8)-2\times(-8)^{2}-137\
=&256-2\times64 - 137\
=&256 - 128-137\
=&-9
\end{align*}
$$
## Step2: Evaluate $\lim_{x
ightarrow - 8}x^{2}+16x + 55$
Substitute $x=-8$ into $x^{2}+16x + 55$.
$$
\begin{align*}
&(-8)^{2}+16\times(-8)+55\
=&64-128 + 55\
=&-9
\end{align*}
$$
## Step3: Apply the Squeeze Theorem
Since $-32x - 2x^{2}-137<g(x)<x^{2}+16x + 55$ and $\lim_{x
ightarrow - 8}(-32x - 2x^{2}-137)=\lim_{x
ightarrow - 8}(x^{2}+16x + 55)=-9$, by the Squeeze Theorem, $\lim_{x
ightarrow - 8}g(x)=-9$.
# Answer:
-9

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Question

Explanation:

Step1: Evaluate $\lim_{x

Step2: Evaluate $\lim_{x

Step3: Apply the Squeeze Theorem

Answer: