Find, in ascending powers of xxx, the first three non-zero terms of the binomial series expansion of
1+3x23∣x∣<13 \sqrt[3]{1 + 3x^2} \quad \quad |x| < \frac{1}{\sqrt{3}} 31+3x2∣x∣<31giving each coefficient as a simplified fraction.
Use the expansion from part (a) with x=12x = \frac{1}{2}x=21 to find a rational approximation to k⋅73k \cdot \sqrt[3]{7}k⋅37, where kkk is a constant you must determine.
