Question

What is the limit as `x` approaches infinity of `(x^2-4)/(2x-4x^2)`?

Answer 1

Answer 2

`-1/4`

Explanation:

`"divide terms on numerator/denominator by the highest"`
`"power of x, that is "x^2`

`rArr(x^2/x^2-4/x^2)/((2x)/x^2-(4x^2)/x^2)=(1-4/x^2)/(2/x-4)`

`rArrlim_(xtooo)(x^2-4)/(2x-4x^2)`

`=lim_(xtooo)(1-4/x^2)/(2/x-4)`

`=(1-0)/(0-4)=-1/4`