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

Question

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

UpStudy AI · Accepted Answer

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

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

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

**Answer:** $$ f(-10) = -8.054 $$

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

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

**Answer:** $$ f(-20) = -8.007 $$

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

For large negative values of $$ x $$, the highest degree terms dominate:

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

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

### Summary

$$
\begin{align*}
\text{(A)}\ & f(-10) = -8.054 \
\text{(B)}\ & f(-20) = -8.007 \
\text{(C)}\ & \lim_{x \to -\infty} f(x) = -8 \
\end{align*}
$$
$$ \begin{align*} \text{(A)}\ & f(-10) = -8.054 \ \text{(B)}\ & f(-20) = -8.007 \ \text{(C)}\ & \lim_{x \to -\infty} f(x) = -8 \ \end{align*} $$

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

Upstudy AI Solution

Answer

Solution

(A)

(B)

©

Summary

Beyond the Answer

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