Question

How do you find `lim (1-2t^-1+t^-2)/(3-4t^-1)` as `t->0`?

Answer 1

`Lim_"t->0"(1-2t^-1+t^-2)/(3-4t^-1)=±oo` depending on if `t->+oo` or `t->-oo`

Explanation:

`Lim_"t->0"(1-2t^-1+t^-2)/(3-4t^-1)`
`=Lim_"t->0"(t²-2t+1)/(3t²-4t)`
`=Lim_"t->0"-1/(4t)`
`=±oo` depending on if `t->+oo` or `t->-oo`
\0/ here's our answer!