Questions: Find each function value and the limit for f(x) = (7 x^4 - 14 x^2) / (10 x^5 + 5). Use -∞ or ∞ where appropriate. (A) f(-6) (B) f(-12) (C) lim x → -∞ f(x)

Transcript text: Find each function value and the limit for $f(x)=\frac{7 x^{4}-14 x^{2}}{10 x^{5}+5}$. Use $-\infty$ or $\infty$ where appropriate. (A) $f(-6)$ (B) $f(-12)$ (C) $\lim _{x \rightarrow-\infty} f(x)$

Solution

Solution Steps

Step 1: Evaluating Function Values

For x = -6, f(x) = -0.11 For x = -12, f(x) = -0.0575

Step 2: Finding the Limit as x Approaches -Infinity

The highest power in the numerator is 4 and in the denominator is 5. Since the highest power in the numerator is less than in the denominator, the limit is 0.