Question

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

Answer 1

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.