Question

Find the limit or show that it does not exist for:

Limit as X approached infinity

X^4-3X^2+X
----------------
X^3 - X + 2

Answer 1

divide top and bottom by x^4

= lim (1 - 3/x^2 + 1/x^3)/(1/x + 1/x^3 + 2/x^4)

as x-->∞
all the terms with x at the bottom ---> 0
so we have

limit (1 -0 + 1)/(0-0+0)
= lim 1/0

which is undefined or infinitely large.