Question

How do you find the limit of `(2x-1)^3` as `x->0`?

Answer 1

`lim_(x->0) (2x-1)^3 = -1`

Explanation:

Let `f(x) = (2x-1)^3`, then f(x) is continuous `AA x in RR` and the limit is not of an indeterminate form;

`:. lim_(x->0) (2x-1)^3 = f(0)`
`:. lim_(x->0) (2x-1)^3 = (-1)^3`
`:. lim_(x->0) (2x-1)^3 = -1`