Calendar: 1890-1891 Page 765

mb ENGINEERING DEPARTMENT cui and the numbers of the series so formed are 18 and 48 find and the three terms of the G- £500 20ץ Τ 0ו per cent per annum compound interest If xf C0 r2 Ckxn prove C0 -f Cx C2 ---- Cn and if χ 2ע Λ0 Λ Λ ---- 2n 2tt prove יי 0η 2- 34λ -1 15 Prove that the terms of the fourth degree in the product r2 r3 tA ifi are equal to י י 16 Express r2 7x -f 12 Α Β in the form--k 4- jind 3י ג 3' r2 Cx ----in the form- 4- -- -4- -- ι -1 λ λ x-1 r-1 17 With 141 panes of glass what is the greatest number of windows that can be filled some of which have 12 and some of which have panes integral Calculus If the velocity of body moving in straight line be 10 feet per second at the end of the first second of its motion and if at any time its velocity be proportional to the cube root of the time it has been moving shew from the principles of the Integral Calculus that at the end of seconds it will have described 120 feet Explain how it is that an arbitrary constant is introduced by integration