Question

How do you find the limit of `f(x) = (x^2 - 1) / ( x + 1) ^2` as x approaches 0?

Answer 1

`lim f(x) = -1` as `x -> 0`

Explanation:

`f(x) = (x^2-1)/(x+1)^2`
`f(x) = ((x+1)(x-1))/((x+1)(x+1)`
`f(x) = (x-1)/(x+1)`

`So, lim f(x) = (0-1)/(0+1) = -1` as `x` goes to zero.