Calendar: 1890-1891 Page 763

ENGINEERING DEPARTMENT CI Sum the following series to η terms sin sin β -f sin From the result deduce the sum of ci ci -f ct 2$ f- to η terms 10 Assuming the binomial expansion for obtain two trigonometrical series by substituting cos β for and sin θ for Utffcvcnttat Calculus Define the differential coefficient of one quantity with respect to another of which it is function and shew that it affords measure of the rate of change of the first compared with that of the second Shew that the differential coefficient of constant is zero and that Prove that ί log six2 log 50 dn 11 12 ץ J- log 4λ ך-י- ץ י ζ 11 ο If py2 2y and express in terms dz dz of a- and verify that τ Shew that sin fl α sin λ £ Prove sin has one of the four values sin dx cos and distinguish between the cases Assuming that can be expanded in ascending powers of obtain Maclaurin's expansion Find by Maclaurin's theorem the development of x2 in ascending powers of 5