# Calendar: 1866-1867 Page 469

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GENERAL LITERATURE AND SCIENCE 471 Prove Maclaurin's Theorem and expand hy it as far as e1 -f- ib du If ך tan tan χ κ -1 jab a' dx cos22 sin's Expand sin χ and cos χ according to the powers of and prove sin 2x sin χ -4- χ cos χ--sin χ cos χ 4- sin χ &c τ 24י τ Evaluate the vanishing fractions V3 a2 ן -- -ך when χ י sin 2ז 8ec log when χ 10 Expand tan-1 Λ to the 4th power of 11 If show how to find the maximum and mini- mum valnes of and how to distinguish between them find these values if χ ג -3 n- Sa χ 2a sin χ cos 12 Find the values of χ and which will make κ maximum when xz y2 c2 and -j 13 Given the surface of cylindrical vessel without lid find its form that it may contain the greatest quantity of fluid

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