1 and 1/8

er yeah, AIM convo

explanation for #1:

Ignore all lower order terms. In the numerator, ignore EVERYTHING except the x^8 term, and in the denominator, ignore EVERYTHING except the x^4 term. EVERYTHING else is insignificant. Thus, you have:

sqrt(4x^8)
    2x^4

Which reduces to 1.

You can do this because you're taking an infinity limit. When x gets huge, x^8 is much larger than x^3, and so on. Thus, you only consider the highest-order terms.