Hyperbolic Functions
The Hyperbolic Sine, Hyperbolic Cosine & Hyperbolic Tangent
The Inverse Hyperbolic Cotangent, Hyperbolic Secant & Hyperbolic Cosecant
Values
Remember Logarithmic Identities ( Calculus I )
Logarithmic Identities II
Identities
Proofs Identity (1)
Proofs Identity (2)
Proofs Identity (3)
Proofs Identity (4)
Proofs Identity (5)
Proofs Identity (6)
Proofs Identity (7)
Derivatives of Hyperbolic Functions
Proofs (1) (sinhx)’ = coshx (2) (coshx)’ = sinhx
Proofs (3) (tanhx)’ = sech2x
Proofs (4) (cothx)’ = -csch2x
Proofs (5) (sechx)’ = - sechx tanhx
Proofs (5) (cschx)’ = - cschx cothx
Integrals Involving hyperbolic Functions
Examples I
Examples II
Examples III
Examples IV
Examples V
Graphs of Hyperbolic Functions
Graphs of Exponential Functions Functions
Graphs of Exponential Functions
f(x) = Cosh x
f(x) = cosh x = (½)ex + (½) e-x as x → ∞ the values f(x) → ∞ following (½)ex as x → - ∞ the values f(x) → ∞ following (½) e-x
f(x) = sinh x
f(x) = tanh x
f(x) = secx