Inv Hyperbolic Functions

# Inv Hyperbolic Functions - Inverse Hyperbolic Functions The...

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Unformatted text preview: Inverse Hyperbolic Functions The Inverse Hyperbolic Sine, Inverse Hyperbolic Cosine & Inverse Hyperbolic Tangent R f range f dom x x g function the of iverse The hx x f R f range R f dom x x g function the of iverse The hx x f f range f dom x x x g function the of iverse The hx x f =- = = = = = = = ∞ = ∞ = ≥ = = , ) 1 , 1 ( tanh ) ( : arctan ) ( . 3 , sinh ) ( : arcsin ) ( . 2 ) , [ , ) , 1 [ ; cosh ) ( : arccos ) ( . 1 The Inverse Hyperbolic Cotangent, Inverse Hyperbolic Secant & Inverse Hyperbolic Cosecant } { , } { csc ) ( : csc ) ( . 3 } { , ) , 1 ( ) 1 , ( , coth ) ( : coth ) ( . 2 ) , [ , ] 1 , ( ; sec ) ( : sec ) ( . 1- =- = ≠ = =- = ∞--∞ = ≠ = = ∞ = = ≥ = = R f range R f dom x hx x g function the of iverse The hx arc x f R f range U f dom x x x g function the of iverse The x arc x f f range f dom x hx x g function the of iverse The hx arc x f Derivatives of Inverse Hyperbolic Functions 1 1 ) (arcsin . 2 ) , 1 ( ; 1 1 ) (arccos . 1 2 2 + = ′ ∞ ∈- = ′ x h x x hx ) 1 , 1 ( ; 1 1 ) (arctan . 3 2- ∈- = ′ x x hx ) 1 , ( ; 1 1 ) sec ( . 4 2 ∈-- = ′ x x x hx arc ) , 1 ( ) 1 , ( ; 1 1 ) coth ( . 5 2 ∞--∞ ∈- = ′ U x x x arc ; 1 1 ) csc ( . 6 2 ; 1 1 ; 1 1 { 2 2 ≠ +- = = ′ +- + x x x hx arc positive is x x x positive is x x x Proofs ) , 1 ( ; 1 1 sin 1 1 sin 1 sinh , 1 ; cosh arccos : . 1 2 2 ∞ ∈- = = ′ ⇒ = ′ ⇒- = ≥ = ⇒ = x x y y y y x y so and x x y hx y Let 1 1 cosh 1 1 cosh cosh 1 cosh sinh arcsin : . 2 2 2 + = = ′ ⇒ = ′ ⇒ + = = ⇒ = x y y y y negative never is y because root positive the choose We x y so and x y hx y Let )...
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Inv Hyperbolic Functions - Inverse Hyperbolic Functions The...

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