A double inequality for tanhx
Abstract In this paper, we prove that, for x>0 $x>0$, 1−exp(−x2x2+1)<tanhx<1−exp(−x3x3+1)3. $$ \sqrt{1-\exp \biggl(-\frac{x^{2}}{\sqrt{x^{2}+1}} \biggr)}< \tanh x< \sqrt[3]{1-\exp \biggl(- \frac{x^{3}}{\sqrt{x^{3}+1}} \biggr)}. $$This solves an open problem proposed by Ivády....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-020-2289-y |