A chemical engineer is modeling the yield, YYY, of a reaction as a function of the catalyst concentration, ccc. The relationship is given by the formula:
Y(c)=1+6c23∣c∣<16 Y(c) = \sqrt[3]{1 + 6c^2} \quad \quad |c| < \frac{1}{\sqrt{6}} Y(c)=31+6c2∣c∣<61Find, in ascending powers of ccc, the first three non-zero terms of the binomial series expansion of Y(c)Y(c)Y(c), giving each coefficient as a simplified fraction.
Use the expansion from part (a) with c=13c = \frac{1}{3}c=31 to find a rational approximation to k⋅53k \cdot \sqrt[3]{5}k⋅35, where kkk is a constant you must determine.
