Question

I need help for all of them. I don’t understand how to do anything of them and i’m really confused

Answer 1

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

   $\lim_{x \to \infty} f(x) = f(2)$ = 1/2