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 first evaluate \( f(-20) \). Given \( f(x) = \frac{14 - 8x^3}{5 + x^3} \): 1. **Calculate \( f(-20) \)**: \[ f(-20) = \frac{14 - 8(-20)^3}{5 + (-20)^3} \] Calculate \( (-20)^3 = -8000 \): \[ f(-20) = \frac{14 - 8(-8000)}{5 - 8000} = \frac{14 + 64000}{5 - 8000} = \frac{64014}{-7995} \] Approximating: \[ f(-20) \approx -8.004 \] 2. **Evaluate the limit \( \lim_{x \to -\infty} f(x) \)**: As \( x \) approaches \(-\infty\), the leading terms dominate: \[ \lim_{x \to -\infty} f(x) = \lim_{x \to -\infty} \frac{-8x^3}{x^3} = -8 \] So, we get: \[ f(-20) \approx -8.004 \quad \text{and} \quad \lim_{x \to -\infty} f(x) = -8 \] Therefore: - \( f(-20) \approx -8.004 \) (rounded to the nearest thousandth) - \( \lim_{x \to -\infty} f(x) = -8 \)