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  Item Reference: KCLCAL-1875-1876-571

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GENERAL LITERATURE AND SCIENCE 567 Draw the asymptotes of cos6 iinff a2 cosd einfl 13 Integrate 7' dx dx dx av χ sin χ x' 2"χ2 2ax dx 14 If factor be repeated in the denominator of fraction shew how the corresponding partial fractions may be found Integrate Γ dx dx 15 If φ χ be the differential coefficient of ψ shew that the limit of Α φ α φ φ α where --- is when is indefinitely diminished φ δ φ α מ Shew that the limiting value when is indefinitely large of η η י יי" ϊ 2ג 16 Shew how to decompose fraction of the form ifi the dimensions of φ χ being lower thau those of into series of partial fractions If the equation have two equal roots σ shew that the φ χ β corresponding terms in -ל-' are-- --where x-afτ χ 2- Φ and β 3φ' Ρ" φ ן ך 17 Find the area of the loop of the curve 9ax 2a '2 iy -f and the length of the arc measured from the vertex to any point Prove that this length is equal to the intercept of the normal on tbe axis of and that the radius of curvature at any normal point ג-L 2a י
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