91Ó°ÊÓ

Differentiate each of the following functions by the method of differentials, and test the result by the methods of Chapter II. $$ u=x^{3}-3 x+1 $$

Differentiate each of the following functions by the method of differentials, and test the result by the methods of Chapter II. $$ z=\frac{1+x+x^{2}}{2 x} $$

Determine the order of each of the following infinitesimals, referred to \(\alpha\) as the principal infinitesimal: $$ \frac{7 \alpha^{2}}{13-\alpha} $$

If \(\beta\) and \(\gamma\) are infinitesimals of orders \(n\) and \(m\) respectively, show that their product, \(\beta \gamma\), is an infinitesimal of order \(n+m .\)