# Calendar: 1899-1900 Page 760

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CVlii FACULTY OF SCIENCE and from the definition find the differential coefficient with respect to χ of eax and of sin ax Find the ratios of if dx ea9e cos71 cos χ -j- sin eax cosn Β cosn2 10 Prove the rule for the differentiation of function of function and apply it to differentiate with respect to log sin ax sin log sin log ax Also differentiate sin log αχ χ sin log sin 11 particle moves in straight line in such manner that its distance from fixed point in the line at time is Λ 27rt ae sin -ך- Prove that the velocity vanishes at the timetan 27Γ Λ and afterwards at intervals and that the acceleration vanishes at the time -tan-1 --- and afterwards at 27r λ2 47H02 intervals and describe the general character of the motion 12 Trace the curve y2x x- f0 20 and find the area of the portion from χ 2a to χ jjftatfjemato Iementarg Paper YEAK tV Prove without multiplying out that 801620 χ 137034 356156 308430 Hence or otherwise shewr that 238632 3322932 and 469327a are in Arithmetical Progression Define fraction in such way as to shew what are meant by Simplify 3$-lj 5f-3 xl$ x3f-l 5f s-3 -lj י1£ 3£יf Mi' 5f-f-3 lJ 5fx3f lj

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