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2015年4月25日 · So, because $\sinh$ is just a function (or operation or "a thing to do"), which does not depend on its input, I could just as easily have defined it as $$\sinh y = \frac{1}{2}(e^y-e^{-y})$$ or $$\sinh t = \frac{1}{2}(e^t-e^{-t})$$ or even $$\sinh \gamma = \frac{1}{2}(e^\gamma-e^{-\gamma})$$ This approach allows me to use different variable ...

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The hyperbolic sine function, $\sinh(x)$ , is defined by the equation: $$ \sinh(x) = \frac {e^x-e^{-x}} {2}$$ Find a formula for its inverse, $$ \sinh^{-1}(x) $$

2021年11月29日 · $\begingroup$ @GEdgar I too am curious, as how would you get the series for that equation? I imagined we just square root both sides like $\sqrt{\sum_{n=0}^{\infty}(-x^2)^n}$, is there a cleaner expression than this?

So write $$\int\frac{1}{\sinh x}\,dx = \int \mathrm{csch} x\,dx$$ and multiply and divide by $\mathrm{csch} x + \coth x$ in preparation for a change of variable. Share Cite

2018年1月11日 · $\begingroup$ By $\sinh^{-1}(x/a)$ you seem to mean the reciprocal of $\sinh(x/a)$, but the usual meaning of that notation is the arc-hyperbolic-sine which is the inverse function of hyperbolic sine. Which do you actually want?

$\sinh^{-1}(x)$ has nothing to do with $\tan^{-1}(x)$, it doesn't hint you to find a correlation between them, it hints you to use the same method for solving the integral.

2019年4月17日 · I am trying to solve $\sinh z = i$; this has to result in $2\pi n + (1/2) \pi i$. When applying the exponential form of $$\sinh z = \frac{e ^ z - e ^ {-z}} 2$$ and later the quadratic equation, this does not give me the result as described above.

The expansion of $\sinh^{-1}(x)$ for $|x|>1$ Ask Question Asked 7 years, 3 months ago. Modified 5 months ago.