Expand 1+2x3\sqrt[3]{1+2x}31+2x in ascending powers of x x\,x up to and including x3 x^3\,x3 and state the set of values of x x\,x for which the expansion is valid.
Use your expansion to find an approximation for 1.13\sqrt[3]{1.1}31.1 to 5 decimal places.
