Calendar: 1872-1873 Page 528

general literature and science 529 Prove that the limit of the error caused by stopping at the th term of Taylor's series is -MXA when β lies between and Investigate the conditions that function of one independent variable may be maximum or minimum Describe the maximum ellipse about given rectangle If ν and u' v' be functions of and θ the rectangular and polar co-ordinates of any point such that it' cos θ v' sin θ sinfl ן cosO prove that in dv u' fin' dtf dx dy dr י" Υ ΊΓθ If φ χ and χ both vanish when χ prove that φ φ' α Show that when or Also find the limit when χ of Λ log Eliminate the circular and logarithmic functions from the equation sin log χ and if χ tan change the inde- pendent variable from χ to ζ in I-0 If be the rectangular coordinates of any point on plane curve be the arc measured from fixed point and ρ the radius of curvature prove that