Calendar: 1878-1879 Page 593

GENERAL LITERATURE AND SCIENCE 591 when χ increases without limit Prove Maclauren's theorem and apply it to expand tan-I τ Find the rath differential co-eificient of Or2 a2 In the curve -J- cosiJ show that the length of the normal is minimum when it is perpendicular to the initial line If χ change the variable from χ to in the equation xdy df dx Trace the curve 3a 2a 10 If Θ be rectangular and polar co-ordinates of the same point prove that tPu du Pu Cftu ipu du df dx ay r2 dr1 d& dr dr du drde τ d6 11 Find the point of inflection in the curve whose equation 13 2a y2 ah 12 Show that the evolute of the curve rf yi ai is similar curve 13 The directrix and one extremity of the minor axis of series of ellipses are given prove that the envelope of the ellipses is circle 14 Explain the meaning of the symbol dx and show how its value may be found Integrate Va2 xdx x'dx 'tan θ fcr lanT