Questions: Find each function value and the limit for f(x) = (5x^4 - 10x^2) / (6x^5 + 3). Use -∞ or ∞ where appropriate. (A) f(-6) = -0.131 (Round to the nearest thousandth as needed.) (B) f(-12) = -0.068 (Round to the nearest thousandth as needed.) (C) lim x→-∞ f(x) (A) f(-6) = -0.131 (Round to the nearest thousandth as needed.) (B) f(-12) = -0.068 (Round to the nearest thousandth as needed.) (C) Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. lim x→-∞ (5x^4 - 10x^2) / (6x^5 + 3) = □

Find each function value and the limit for f(x) = (5x^4 - 10x^2) / (6x^5 + 3). Use -∞ or ∞ where appropriate.
(A) f(-6) = -0.131
(Round to the nearest thousandth as needed.)
(B) f(-12) = -0.068
(Round to the nearest thousandth as needed.)
(C) lim x→-∞ f(x)
(A) f(-6) = -0.131
(Round to the nearest thousandth as needed.)
(B) f(-12) = -0.068
(Round to the nearest thousandth as needed.)
(C) Select the correct choice and, if necessary, fill in the answer box to complete your choice.
A. lim x→-∞ (5x^4 - 10x^2) / (6x^5 + 3) = □

Transcript text: Find each function value and the limit for $f(x)=\frac{5 x^{4}-10 x^{2}}{6 x^{5}+3}$. Use $-\infty$ or $\infty$ where appropriate. (A) $f(-6)$ (B) $f(-12)$ (C) $\lim _{x \rightarrow-\infty} f(x)$ (A) $f(-6)=-0.131$ (Round to the nearest thousandth as needed.) (B) $f(-12)=-0.068$ (Round to the nearest thousandth as needed.) (C) Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. $\lim _{x \rightarrow-\infty} \frac{5 x^{4}-10 x^{2}}{6 x^{5}+3}=\square$

Solution

Solution Steps

Step 1: Evaluating Function Values

For x = -6, f(x) = -0.131 For x = -12, f(x) = -0.068

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.