Fungsi hiperbolik: Perbedaan antara revisi
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[[Berkas:Hyperbolic functions-2.svg|jmpl|ka|200px|Fungsi hiperbolik]]
'''Fungsi hiperbolik''' adalah salah satu hasil [[kombinasi]] dari fungsi-fungsi [[eksponen]]. Fungsi hiperbolik memiliki rumus. Selain itu memiliki [[invers]] serta turunan dan anti turunan fungsi hiperbolik dan inversnya.<ref name="Dwi Perpus Unnes">{{cite web|date=|title=FUNGSI HIPERBOLIK DAN INVERSNYA|url=http://lib.unnes.ac.id/990/|work=|publisher=DIGILIB UNNES|format=|doi=|accessdate=2014-05-28|archive-date=2019-08-15|archive-url=https://web.archive.org/web/20190815042811/https://lib.unnes.ac.id/990/|dead-url=no}}</ref>
== Definisi ==
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di mana {{math|sgn}} adalah [[fungsi tanda]].
Jika <math>x \ne 0</math>, maka<ref>{{cite web |title=Prove the identity |url=https://math.stackexchange.com/q/1565753 |website=[[StackExchange]] (mathematics) |accessdate=24 January 2016 |archive-date=2023-07-26 |archive-url=https://web.archive.org/web/20230726134114/https://math.stackexchange.com/questions/1565753/prove-the-identity-tanh-left-fracx2-right-frac-coshx-1-sinhx |dead-url=no }}</ref>
:<math> \tanh\left(\frac{x}{2}\right) = \frac{\cosh x - 1}{\sinh x} = \coth x - \operatorname{csch} x </math>
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=== Pertidaksamaan ===
Pertidaksamaan berikut sangat berguna dalam statistik, yaitu <math>\operatorname{cosh}(t) \leq e^{t^2 /2}</math><ref>{{cite article|last1=Audibert|first1=Jean-Yves|title=Fast learning rates in statistical inference through aggregation|date=2009|publisher=The Annals of Statistics|page=1627}} [https://projecteuclid.org/download/pdfview_1/euclid.aos/1245332827] {{Webarchive|url=https://web.archive.org/web/20230726134112/https://projecteuclid.org/journalArticle/Download?urlId=10.1214%2F08-AOS623&isResultClick=False |date=2023-07-26 }}</ref>
== Fungsi invers sebagai logaritma ==
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