Calendar: 1890-1891 Page 764

Cll ENGINEERING DEPARTMENT Prove that maximum and minimum values of any function occur alternately Find the values of χ for which x2 is maximum Shew that the greatest and least radii from the origin to the curve ax2 2hxy by2 lie in the directions of the lines xy x2 y2 Shew that the equations of the tangent and normal at the point of curve are respectively Y-y X-x and r-y -if X- ax ay JT being current coordinates If th tangent at point Ρ of any curve meets the axes of χ and in Τ and Tf and the normal at Ρ meets the axes in Ν and Nf respectively then shew that tan PTN FN algebra 10 If ί is series of fractions in order of ρ magnitude prove that the numerical value of the fraction jg between those of and ί Apply this τ ρ ρ λ"ρ-1 ΧΡ Χ9 XQ-l theorem to -ץ -- -ך -ך χ being positive and greater than ρ and positive integers and ρ to ן xv shew that pi 11 The sixth term of an is 19 and the 12 term is 37 find the first term and the common difference How must be taken that the be 69 12 Insert geometric means between and 405 Three terms of are increased each by the same