Find the limits (that is, end behaviors) below. Enter INFINITY and -INFINITY for ∞∞ and −∞−∞, respectively.

Question

Find the limits (that is, end behaviors) below. Enter INFINITY and -INFINITY for ∞∞ and −∞−∞, respectively.

(a) As 𝑥→∞x→∞,   −4𝑥(𝑥^2+2)/3+3𝑥^4→  

b) As 𝑥→−∞,   6𝑥(𝑥−8)(𝑥+6)/9+8𝑥^3→

Answer 1

a) + infinity. the highest degree term dominates

that's assuming you meant [-4x(x^2+2)/3] + 3x^4

if you meant a denominator of (3+3x^4) then the limit is -4x^3/3x^4 approaches zero

b) - infinity,

assuming you meant [6x(x-8)(x+6)/9] + 8x^3

if you meant a denominator of 9+8x^3 then the limit would be 6x^3/8x^3 = 6/8= 3/4

the way you've written it

the correct limits are a) +infinity b)-infinity