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

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:** \( f(-10) = -8.054 \) --- ### (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:** \( f(-20) = -8.007 \) --- ### (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:** \( \lim_{x \to -\infty} f(x) = -8 \) --- **Summary:** - **(A)** \( f(-10) = -8.054 \) - **(B)** \( f(-20) = -8.007 \) - **(C)** \( \lim_{x \to -\infty} f(x) = -8 \)