Calendar: 1882-1883 Page 629

626 GENERAL LITERATURE AND SCIENCE weight and at the other movable pulley weight IF over the latter hangs string with weights at its ends find the accelerations of For example 12 lbs lib Ρ lbs lbs tffmnttal anK jhitcgral Calculus Define differential coefficient without the use of any symbols and prove without the use of any formula that the differential coefficient of the area of circle with respect to the radius is equal to the circumference Find from first principles the differential coefficients of coscc and sec Also differentiate cos sec sec cosa sec cosx and a2 sin χ cot Write and illustrate by diagrams the different cases that may arise Evaluate when χ sec sin χ2 and χ3 χ 10g If χ rcos rsin give geometrical inlerpreta- dr νάθ ב dr dr tions of י and shew that dx dy dx ctr Why is this not inconsistent with Find the asymptotes of dx dy 2a and trace the curve Trace the curves ahf 2a sin φ αύιιδθ log sin Θ