A materials scientist models the longitudinal strain ϵ\epsilonϵ in a composite beam using the function ϵ(h)=(14−3h)12\epsilon(h) = \left(\frac{1}{4} - 3h\right)^{\frac{1}{2}}ϵ(h)=(41−3h)21, where hhh is the applied load factor and ∣h∣<112|h| < \frac{1}{12}∣h∣<121. Find the first 4 terms, in ascending powers of hhh, of the binomial expansion for ϵ(h)\epsilon(h)ϵ(h), giving each coefficient in its simplest form.
By substituting h=1100h = \frac{1}{100}h=1001 into the expansion found in (a), find an approximation for 22\sqrt{22}22.
Give your answer in the form ab\frac{a}{b}ba where aaa and bbb are integers to be found.
