Question

How do you evaluate the limit `(x^5-1)/(x-1)` as x approaches `1`?

Answer 1

The expression `=5`

Explanation:

`x^5-1` is divisible by `x-1`

You must make a long division

`(x^5-1)/(x-1)=x^4+x^3+x^2+x+1`

Let `f(x)=(x^5-1)/(x-1)=x^4+x^3+x^2+x+1`

Then `f(1)=1+1+1+1+1=5`

graph{(x^5-1)/(x-1) [-9.92, 10.08, -3, 7]}