Find each function value and the limit for $$ f(x)=\frac{14-8 x^{3}}{5+x^{3}} $$. Use - $$ \infty $$ or $$ \infty $$ where appropriato $$ \begin{array}{lll} ext { (A) } f(-10) & ext { (B) } f(-20) & ext { (C) } \lim _{x ightarrow-\infty} f(x)\end{array} $$ $$ \begin{array}{ll} ext { (A) } f(-10)=-8.054 \ ext { (Round to the nearest thousandth as needed.) } \ ext { (B) } f(-20)=\square & \square\end{array} $$ (Round to the nearest thousandth as needed.)

Question

Find each function value and the limit for $$ f(x)=\frac{14-8 x^{3}}{5+x^{3}} $$. Use - $$ \infty $$ or $$ \infty $$ where appropriato $$ \begin{array}{lll}	ext { (A) } f(-10) & 	ext { (B) } f(-20) & 	ext { (C) } \lim _{x ightarrow-\infty} f(x)\end{array} $$ $$ \begin{array}{ll}	ext { (A) } f(-10)=-8.054 \ 	ext { (Round to the nearest thousandth as needed.) } \ 	ext { (B) } f(-20)=\square & \square\end{array} $$ (Round to the nearest thousandth as needed.)

UpStudy AI · Accepted Answer

Let's evaluate the function $$ f(x) = \frac{14 - 8x^3}{5 + x^3} $$ for the given values and find the limit as $$ x $$ approaches $$-\infty$$.

### (A) $$ f(-10) $$

$$
f(-10) = \frac{14 - 8(-10)^3}{5 + (-10)^3} = \frac{14 + 8000}{5 - 1000} = \frac{8014}{-995} \approx -8.054
$$

**Rounded to the nearest thousandth:**  
$$ f(-10) = -8.054 $$

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### (B) $$ f(-20) $$

$$
f(-20) = \frac{14 - 8(-20)^3}{5 + (-20)^3} = \frac{14 + 64000}{5 - 8000} = \frac{64014}{-7995} \approx -8.007
$$

**Rounded to the nearest thousandth:**  
$$ f(-20) = -8.007 $$

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### (C) $$ \lim_{x \to -\infty} f(x) $$

To find the limit as $$ x $$ approaches $$-\infty$$, consider the dominant terms in the numerator and denominator:

$$
\lim_{x \to -\infty} \frac{14 - 8x^3}{5 + x^3} = \lim_{x \to -\infty} \frac{-8x^3}{x^3} = -8
$$

**Limit:**  
$$ \lim_{x \to -\infty} f(x) = -8 $$

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**Summary:**

- **(A)** $$ f(-10) = -8.054 $$
- **(B)** $$ f(-20) = -8.007 $$
- **(C)** $$ \lim_{x \to -\infty} f(x) = -8 $$
$$ f(-10) = -8.054 $$, $$ f(-20) = -8.007 $$, and $$ \lim_{x \to -\infty} f(x) = -8 $$.

Find each function value and the limit for . Use - or where appropriato

(Round to the nearest thousandth as needed.)

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(B)

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Find each function value and the limit for . Use - or where appropriato (Round to the nearest thousandth as needed.)