lim x-> infinity (7x^(5/3)-2x^(1/3)+6)/(-2x^(8/5)-5x+square root(x))

Answer 1

As x->∞, only the highest powers are relevant, so we wind up with the limit of

7x^(5/3) / -2x^(8/5)
= -7/2 x^1/15 -> -∞

Or, you can divide top and bottom by x^(5/3) and then throw away all the fractions with x in the bottom