Calendar: 1865-1866 Page 533

GENERAL LITERATURE AND SCIENCE 53Γ SECOND YEAR SCHOLARSHIP EUnuntarp Stffmnttal Calculus Define the term function and distinguish between implicit explicit algebraical and transcendental functions illustrating each by an example Define differential coefficient and prove the rules for finding that of product of quotient of function of function ן du χ sin-1 If χ Vl x2 sin then dx 1- d"u Jf are then χ- dx" 1a bx Expand according to the powers of log --ן χ du If κ show that V2 makes If ecx cot χ maximum cos χ sin 18 Expand ecosX according to the powers of the 4th term 1S lj 6' If then 10 If and ί be proper fraction prove that Λ θ 11 Explain how the limiting values of functions in the case of may be found apply the method to the question 12 12 When χ find the value of the fraction χ 2a2 g" 2y V- tan sin 13 Evaluate ד- when χ and find the limiting sin tan י values of sin and cos cosec βχ for the values of χ in both cases