calculus - Inverse of cosh (x) - Mathematics Stack Exchange
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Deriving $\\cosh^{-1}{x}=\\ln\\left(x+\\sqrt{x^2-1}\\right)$
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Find the solutions of $\\cosh(z)=1$ - Mathematics Stack Exchange
2019年12月16日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
In proving $\\cosh(\\sinh^{-1}(x))=\\sqrt{1+x^2}$ don't we need ...
2022年7月27日 · $\begingroup$ The reason why we take the positive square root for $\cosh$ is partially that $\cosh\ge0$ and it's probably inherent to the proof you're reading, but it should be …
Range of Real Inverse Hyperbolic Cosine -- can it be negative?
2021年1月2日 · $\begingroup$ Well okay, but the 1968 edition (the only one I have immediate access to) actually has $\cosh^{-1}$ rather than $\operatorname{arcosh}$ ... so in light of what …
geometry - How to find $\cosh(\operatorname{arsinh}(f(x ...
2024年3月21日 · With the regular trig functions, if I ever end up with something like $\operatorname{trig}_1(\operatorname{arctrig}_2(f(x))$, where $\text{trig}_1$ and …
trigonometry - Calculate cosh 1 correct to 6 decimal places ...
You can simplify cosh 1 to $$ cosh(1) = 1/2 (1/e+e^1) $$ And use the following approximation of e (good for 9 decimal digits): $$ \frac{271\,801}{99\,990} $$ Alternatively you can approximate e …
Limit of a Cosh function - Mathematics Stack Exchange
Evaluate $$\lim_{t\to\infty} (\cosh x)^{1/x}.$$ I tried to use L'Hopital's but I think I made a mess of the differentiation, and the differentiation doesn't seem like it'll help much. calculus limits
Laurent series for coshz - Mathematics Stack Exchange
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calculus - Prove that $\cosh^{-1}(1+x)=\sqrt{2x}(1 …
2015年12月23日 · The trick is to recognize the $1/\sqrt x$ singularity in the derivative of the function of interest and transform the series into a series in $\sqrt x$.