| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2010 |
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| Session | November |
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| Topic | Hyperbolic functions |
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1 The curve \(C\) has equation \(y = \frac { 1 } { 4 } \left( \mathrm { e } ^ { 2 x } + \mathrm { e } ^ { - 2 x } \right)\). Show that the length of the \(\operatorname { arc }\) of \(C\) from the point where \(x = 0\) to the point where \(x = \frac { 1 } { 2 }\) is \(\frac { \mathrm { e } ^ { 2 } - 1 } { 4 \mathrm { e } }\).