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7.7 Hyperbolic Functions

7.7 Hyperbolic Functions. Math 6B Calculus II. Definition of Hyperbolic Functions. Hyperbolic Cosine (cosh) Hyperbolic Sine (sinh) Other Hyperbolic Functions. Hyperbolic Identities. sinh (- x ) = - sinh x cosh (- x ) = cosh x cosh 2 x – sinh 2 x = 1 1 – tanh 2 x = sech 2 x

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7.7 Hyperbolic Functions

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  1. 7.7 Hyperbolic Functions Math 6B Calculus II

  2. Definition of Hyperbolic Functions • Hyperbolic Cosine (cosh) • Hyperbolic Sine (sinh) • Other Hyperbolic Functions

  3. Hyperbolic Identities • sinh(-x) = -sinhx • cosh(-x) = coshx • cosh2x – sinh2x = 1 • 1 – tanh2x = sech2x • sinh(x+y) = sinhx coshy + coshx sinhy • cosh(x+y) = coshx coshy + sinhx sinhy

  4. Inverse Hyperbolic Functions

  5. Inverses of the Hyperbolic Functions Expressed as Logarithms

  6. Derivatives of Inverse Hyperbolic Functions

  7. Derivatives of Inverse Hyperbolic Functions

  8. Integrals of Inverse Hyperbolic Functions

  9. Integrals of Inverse Hyperbolic Functions

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