# Math

Find the Limit of x->1+
x^3 + 1/ x - 1 =?

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1. lim (x^3 - 1) / (x - 1)
x -> 1

To evaluate this limit, we must remove the [0/0] form of it. If we were to plug in x = 1 now, we would get [0/0], which alone tells us the limit may exist.

The numerator factors as a difference of cubes.

lim (x - 1)(x^2 + x + 1) / (x - 1)
x -> 1

And look how (x - 1) cancels out.

lim (x^2 + x + 1)
x -> 1

It is now safe to evaluate the limit at x = 1.

1^2 + 1 + 1
1 + 1 + 1
3

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