Calendar: 1871-1872 Page 520

520 general literature and science 15 Prove De Moivre's theorem Deduce the expansions of cos and sin in powers of 16 Sum the series sin sin θ φ --sin β 2ψ to infinity δ cos0 cos20 cos θ cosrafl Show that β π θ 2π θ η η sin θ 2"י sin sin sin-י sin- η η η η II -uiflewnttal anil fntrgral Calculus ice Differentiate from first principles 10ge sin-'f ax and find by the ordinary rules the first derived function of λ 4- tan"1 מב-צ-- Find the rth differential coefficient of cos Find the limit of -j as χ increases indefinitely Obtain also the limits of -J χ £5 an when χ becomes infinite Ify φ ζ and prove that dy dy dz cQz dz dx Find an expression for the remainder after the first terms of the expansion of by Taylor's theorem