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Hyperbolic functions (CheatSheet)

Hyperbolic functions (CheatSheet)1 IntroFor historical reasons Hyperbolic functions have little or no room at all in the syllabus of a calculuscourse, but as a matter of fact they have the same dignity as trigonometric functions . Unfortu-nately this can be completely understood only if you have some knowledge of the complex speaking ordinary trigonometric functions are trigonometric functions of purely real num-bers, and Hyperbolic functions are trigonometric functions of purely imaginary numbers. For themoment we have to postpone this discussion to the end of Calc3 or Calc4, but still we should beaware of the fact that the impressive similarity between trig formulas and Hyperbolic formulas isnot a pure of the formulas that follow correspond precisely to a trig formula or they differ by at mosta change of sign. For each formula I will explicitly state if some change of sign occurs or not (thedifferent sign is marked in green).

the formulas that we have seen so far; and if you really don’t know how to integrate an hyperbolic function, just remember that an hyperbolic function can be written using the exponential, and usually functions containing the exponential are easy to integrate.

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