# Calendar: 1875-1876 Page 569

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GENERAL LITERATURE AND SCIENCE 565 sin tan and ax Find the differential coefficient with regard to of the expression llog un 2x- tan-1 and prove that the result £sin 20 if tantf x3 Prove that dy dx and that dy dz dx dz dx' χ being functions of Find the differential coefficients of and sin-lg tan-tQ log tan-1 -- a2 b'1 If is function of χ which vanishes when χ and when χ and is also continuous between the same limits prove that ι must also vanish for some value of χ between 11 and cx If cos prove that 27--f- 64ce Find an expression for the difference between ψ χ and the first terms of its expansion by Taylor's theorem Shew that Find the value of 2x cotz cos -I- cos-- cos -- when χ

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