Answer:
steps below
Step-by-step explanation:
1) f(x) = (-3ax⁴ + ax² +x) / (2x⁴ + x³ - ax² + 8x) ... degree of the denominator = degree of the numerator (-3a) / 2 = 5 / 4
-12a = 10
a = - 5/6
2) 3-n > n+ 10 ... degree of the denominator < degree of the numerator
2n < -7
n < - 3.5
The largest inter value is -4
3) f(x) = (x²+3x-4) / (2x²+7x-10)
f(2) = (2²+3*2-4) / (2*2²+7*2-10) = 6 / 12 = 1/2
x->∞ : divide x² both numerator and denominator, any number/ x -> 0
f(x) = (1 + 3/x - 4/x²) / (2 + 7/x - 10/x) = (1 + 0 - 0) / (2 + 0 - 0) = 1/2
[tex]\lim_{x \to \infty} f(x) = f(2)[/tex] = 1/2
