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Hyperbolic Funcs

# Hyperbolic Funcs - GRAPHS OF HYPERBOLIC FUNCTIONS y = slnhx...

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Unformatted text preview: GRAPHS OF HYPERBOLIC FUNCTIONS y = slnhx y=ooshx .1 INVERSE a HYPERBOLIC FUNCTIONS Ifx = slnh y, theny = slnrr1 a Is called the Inverse hyperbolic slne of x. Slmllarly we deflne the other Inverse hyperbollc functlons. The Inverse hyperbollc functlons are multlple- valued and as In the case of Inverse trlgonometrlc functlons we restrlct ourselves to prlnclpal values for whlch they can be oonsldered as slngle-valued. The followlng list shows the prlnclpal values [unless otherwlse lndlcated] of the Inverse hyperbollc functlons expressed In terms of logarlthmlc functlons whlch are taken as real valued. slnh'1 x = In (x +I/5‘ﬁ) oosh’1 x = In (x + m) tam-1x = Vzln((1 + x)/(1 - x)) (:oth'1 x = V:ln((x + 1)/(x - 1)) sech'1 x = In ( 1]): + :1;_,‘) 0 < x s 1 [sech'1 a; > o Is prlnclpal value] [email protected]<X<@ x z 1 [oosh’1 x > 0 Is prlnclpal value] -1<x<1 X>10fX<-1 (sch‘1 x = In(1/x + "5’, I) x s o GRAPHS OF INVERSE HYPERBOLIC FUNCTIONS y = slnh‘lx y = cosh'lx v ...
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