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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 = 1 2 1 + e + 1 + e 1 + e = 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 , u = e 1 I = e e 1 d u u + 1 = ln (u + 1 ) e e 1 = ln ( e + 1 ) ln 1 + 1 e = ln e + 1 1 + 1 e = ln ( 1 + e ) e ( e + 1 ) = 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 1 sin 2 y = 1 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 x ( 2 sin θ + 1 ) 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 x 1 2 2 + y 2 2 2 = 1 sin 2 θ + cos 2 θ = 1 (x 1 ) 2 + (y 2 ) 2 = 4 (4)

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4. ( a ) (y + 1 ) d y
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Edexcel_WS_C4_PaperH - Worked Solutions Edexcel C4 Paper H...

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