MATH1151 Chapter Notes - Chapter 1: Woodhaven And Cross Bay Boulevards Buses, List Of Bus Routes In Queens, Hyperbolic Function
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Note that cosh x 1 so 0 < sech2x 1. Finally, tanh x = 0 x = 0. y = tanh x x. Derivatives of other hyperbolic functions yperbolic functions: d dx d dx d dx sech x = sech x tanh x cosech x = cosech x coth x coth x = cosech2 x . Recall the graphs of sinh and tanh are increasing functions and hence are one-to-one. cosh however is not one-to-one and so we need to restrict the domain to [0, ). Of course we can get the graphs of these functions by just re ecting the graphs of cosh, sinh and tanh. As on the last slide, you can show that cosh 1 x = n!y + py 2 + 1" = sinh 1 y .
