Calendar: 1873-1874 Page 618

618 THE SCHOOL about the point and the condition that the highest point may be vertically above the point of projection If the cylinder were unrolled into plane what would be the form of the curve assumed by the path of the particle StfTrrcnttal CalruluS Define differential coefficient and find from your definition the differential coefficients with regard to of sin logx and sin sin Ify prove that dy dx dx dy Differentiate with regard to the expressions χ β2 ύή χ2 ί2 log r2 a2 and sin Find the rth differential coefficients of jr3r sin ג and em sin mx Prove that under certain restrictions φ α φ α φ' α 6h ψ α ψ' α ΘΙή' Apply Maclaurin's Theorem to expand in powers of sin emx sin mx finding in each case the rth term If φ χ have maximum or minimum value when χ prove that φ' α or co If dy χ dx find the values of χ which makey maximum or minimum Show how to determine the limiting value of fraction fl which for given value of takes the form φ χ