Edexcel_WS_C4_PaperH

Edexcel_WS_C4_PaperH - Worked Solutions Edexcel C4 Paper H...

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Worked Solutions Edexcel C4 Paper H 1. ( a ) x 1 0 1 1 1 + e 1 1 1 + e 1 1 + 1 1 1 + 1 e 1 1 + 1 e = e e + 1 integral 1 2 ± 1 1 + e + e e + 1 + 2 × 1 2 ² = 1 2 ± 1 + e + 1 + e 1 + e ² = 1 (4) ( b ) let I = # 1 1 1 1 + e x d x put u = e x d u d x = e x d u = e x d x = # 1 1 e x e x + 1 d x when x = 1 ,u = e x =− 1 = e 1 I = # e e 1 d u u + 1 = h ln (u + 1 ) i e e 1 = ln ( e + 1 ) ln ³ 1 + 1 e ´ = ln e + 1 1 + 1 e = ln ± ( 1 + e ) e ( e + 1 ) ² = ln e = 1 (4) 2. ( a ) (i) differentiating implicitly, 1 = e y d y d x d y d x = 1 e y = 1 x (2) (ii) when y = 0, x = e 0 = 1 d y d x = 1 equation of tangent is y 0 = x 1 y = x 1 (2) ( b ) x = sin y 1 = cos y d y d x d y d x = 1 cos y = 1 µ 1 sin 2 y = 1 p 1 x 2 (3) 3. ( a ) d y d x = 2 sin θ 2 cos θ sin θ cos θ equation of tangent is y ( 2 cos θ + 2 ) sin θ cos θ h x ( 2 sin θ + 1 ) i y cos θ 2 cos 2 θ 2 cos θ x sin θ + 2 sin 2 θ + sin θ x sin θ + y cos θ = 2 + 2 cos θ + sin θ (4) ( b ) when θ = π 2 tangent is x + 0 = 2 + 0 + 1 x = 3 (1) ( c ) sin θ = x 1 2 , cos θ = y 2 2 ³ x 1 2 ´ 2 + ³ y 2 2 ´ 2 = 1 h sin 2 θ + cos 2 θ = 1
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This note was uploaded on 06/04/2010 for the course MATH C4 taught by Professor N/a during the Spring '10 term at Cambridge College.

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Edexcel_WS_C4_PaperH - Worked Solutions Edexcel C4 Paper H...

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