Question

Evaluate the limit `lim_(x rarr -1) (x^3-x)/(x-1)`?

Answer 1

`lim_(x rarr -1) (x^3-x)/(x-1) = 0`

Explanation:

`lim_(x rarr -1) (x^3-x)/(x-1) = lim_(x rarr -1) (x(x^2-1))/(x-1)`
`" " = lim_(x rarr -1) (x(x+1)(x-1))/(x-1)`
`" " = lim_(x rarr -1) (x(x+1)`
`" " = (-1)(0)`
`" " = 0`

And we can verify this graphically:
graph{(x^3-x)/(x-1) [-2.579, 1.302, -0.636, 1.304]}