Pertidaksamaan: Perbedaan revisi

10 bita ditambahkan ,  4 bulan yang lalu
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* Untuk bilangan riil '' a '' dan '' b '',
:: <math>\frac{e^b-e^a}{b-a} > e^{(a+b)/2}.</math>
* BialBila ''x'', ''y'' > 0 dan 0 < ''p'' < 1, maka
:: <math>x^p+y^p > \left(x+y\right)^p.</math>
* IfBila ''x'', ''y'', ''z'' > 0, thenmaka
:: <math>x^x y^y z^z \ge \left(xyz\right)^{(x+y+z)/3}.</math>
* IfBila ''a'', ''b'' > 0, thenmaka<ref>{{Cite journal |jstor = 2324012|last1 = Laub|first1 = M.|last2 = Ilani|first2 = Ishai|title = E3116|journal = The American Mathematical Monthly|year = 1990|volume = 97|issue = 1|pages = 65–67|doi = 10.2307/2324012}}</ref>
:: <math>a^a + b^b \ge a^b + b^a.</math>
* IfBila ''a'', ''b'' > 0, thenmaka<ref>{{cite journal|first=S.|last=Manyama|title=Solution of One Conjecture on Inequalities with Power-Exponential Functions|journal=Australian Journal of Mathematical Analysis and Applications|url=https://ajmaa.org/searchroot/files/pdf/v7n2/v7i2p1.pdf|volume=7|issue=2|page=1|date=2010}}</ref>
:: <math>a^{ea} + b^{eb} \ge a^{eb} + b^{ea}.</math>
* IfBila ''a'', ''b'', ''c'' > 0, thenmaka
:: <math>a^{2a} + b^{2b} + c^{2c} \ge a^{2b} + b^{2c} + c^{2a}.</math>
* IfBila ''a'', ''b'' > 0, thenmaka
:: <math>a^b + b^a > 1.</math>
 
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