Calendar: 1886-1887 Page 679

GENERAL LITERATURE AND SCIENCE 681 Wb divergent Show that the series ן- 1- -1 &c is convergent if χ is greater than unity and divergent if χ 11 What is meant by the differential coefficient of function of Prove from first principles that tan sec2 dx Find the value of in the following examples dx loge a2 x2 tan 2x χ 12 If ίψ prove that dJ mu M& dx Find what values of make -- maximum or minimum m2 x2 χ2 χ and find the maximum value of -- x2 χ 13 Find that fraction which exceeds its second power by the greatest possible number 14 Expand 10ge by Maclaurin's theorem 15 Interpret the meaning of in the following cases dx is the ordinate corresponding to an abscissa is the momentum gained by moving body in time is the kinetic energy acquired by body while moving through distance III -4 tomttr1 If one angle of triangle be divided into two equal angles by straight line which also cuts the base the seg- ments of the base shall have the same ratio which the other sides of the triangle have to one another