How do you find the limit of #(x^(4) - 2x + 3)/(4 - 5 x^(3)) # as x approaches #oo#?

1 Answer
Apr 3, 2016

This limit does not exist and is divergent.

Explanation:

Since the given function is a rational one with polynomial numerator and denominator, we may consider only the highest powers of #x# when evaluating the limit at #oo#.

#therefore lim_(x->oo)((x^4-2x+3)/(4-5x^3))=lim_(x->oo)(x^4/(-5x^3))#

#=lim_(x->oo)(x/(-5))#

#=oo#.

Hence this limit does not exist and is divergent.