Question

if ( k(x)=\frac{x^{3}+512}{x + 8} ), complete the table and use the results to find ( lim _{x
ightarrow-8} k(x) ).

complete the table.

(round to three decimal places as needed.)

Explanation:

Step 1: Substitute \(x = - 8.1\) into \(k(x)=\frac{x^{3}+512}{x + 8}\)

$$
LATEXBLOCK0
$$

Step 2: Substitute \(x=-8.01\) into \(k(x)=\frac{x^{3}+512}{x + 8}\)

$$
LATEXBLOCK1
$$

Step 3: Substitute \(x = - 8.001\) into \(k(x)=\frac{x^{3}+512}{x + 8}\)

$$
LATEXBLOCK2
$$

Step 4: Substitute \(x=-7.999\) into \(k(x)=\frac{x^{3}+512}{x + 8}\)

$$
LATEXBLOCK3
$$

Step 5: Substitute \(x=-7.99\) into \(k(x)=\frac{x^{3}+512}{x + 8}\)

$$
LATEXBLOCK4
$$

Step 6: Substitute \(x=-7.9\) into \(k(x)=\frac{x^{3}+512}{x + 8}\)

$$
LATEXBLOCK5
$$

Answer:

\(x\)	\(-8.1\)	\(-8.01\)	\(-8.001\)	\(-7.999\)	\(-7.99\)	\(-7.9\)

As \(x\) approaches \(-8\) from both sides, \(k(x)\) approaches \(192\). So \(\lim_{x
ightarrow - 8}k(x)=192\)