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

Please help and explain, I'm really lost.

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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

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