Find the Limit of x->1+
x^3 + 1/ x - 1 =?
Please help and explain, I'm really lost.
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