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## Homework Statement

This is a question from a past exam paper:

Compute the limit:

lim x→∞

(2x[itex]^{3}[/itex] + x)[itex]/[/itex](3x[itex]^{2}[/itex] − 4x[itex]^{3}[/itex])

## Homework Equations

## The Attempt at a Solution

I really had no idea how to approach this but the solution is:

Hopefully someone can explain to me the method used to obtain this answer.lim x→∞

(2x[itex]^{3}[/itex] + x)[itex]/[/itex](3x[itex]^{2}[/itex] − 4x[itex]^{3}[/itex])

= lim y→0+

(2 + y[itex]^{2}[/itex])[itex]/[/itex](3y − 4)

=

2[itex]/[/itex]−4

= −1[itex]/[/itex]2