Question

find each function value and limit. use - ∞ or ∞ where appropriate. f(x) = (5x³ - 10x²)/(8x⁴ + 4) (a) f(-6) (b) f(-12) (c) lim┬(x→ - ∞)⁡〖f(x)〗 (a) f(-6)=□ (round to the nearest thousandth as needed.)

Explanation:

Step1: Substitute x = - 6 into f(x)

$f(-6)=\frac{5(-6)^{3}-10(-6)^{2}}{8(-6)^{4}+4}$

Step2: Calculate the numerator

$5(-6)^{3}-10(-6)^{2}=5\times(-216)-10\times36=-1080 - 360=-1440$

Step3: Calculate the denominator

$8(-6)^{4}+4=8\times1296 + 4=10368+4 = 10372$

Step4: Calculate the value of f(-6)

$f(-6)=\frac{-1440}{10372}\approx - 0.139$

Answer:

-0.139