Question

How do you find the limit of `(x^5 – 1)/(x – 1)` as x approaches 1?

Answer 1

I got that tends to `5`.

Explanation:

If you try directly using `1` you get the indeterminate form `0/0`. We can use de L'Hospital rule deriving top and bottom and then apply the limit as:
`lim_(x->1)(x^5-1)/(x-1)=lim_(x->1)color(red)((5x^4-0)/(1-0))=`

as `x->1` we get:

`=lim_(x->1)(5x^4-0)/(1-0)=5/1=5`