Calendar: 1875-1876 Page 570

5ββ GENERAL LITERATURE AND SCIENCE lfy e-x cos prove that when χ cos- dz and t- cos prove that when זג Ltg 23 $g £ί£ rfjיי יי dx dxn p0 being greater than What is meant by maximum or minimum value of function of variable If be maximum or minimum value of shew that must be either zero or infinite What criterion distinguishes the maxima from the minima PSP is focal chord of an ellipse shew that when the area of the triangle PCP" is maximum PSP'js the latus rectnm 10 If χ ct change the variable from χ to in the equation Xdx y- Having given prove that being function of the independent variables τ and Vrf Vtfy dtl yds ds dt and d'u d'u -du cPu Pu I2 -- 4' dx" dy2 dt dt ds dsdt 11 The equation of the tangent to curve at the point is du du rf- cr-y --o Find the equations of the normal to the curve xi yi al and of the tangent to the curve x-f-y ή- x-y 2ai which make an angle θ with the axis of 12 Define the polar subtangent and shew how it is employed in determining and drawing the rectilinear asymptotes of curve