Sep 5, 2006 · Swatting a fly with a sledgehammer! Multiply both numerator and denominator of [tex] = \lim_{x\rightarrow\infty} \frac{e^x - e^{-x}}{e^x + e^{-x}}[/tex]

May 30, 2010 · (as we know that tanh(x) is an aodd function) and then multiply both sides by the series for cosh(x) and then solve for a1, a3, etc by equating the coefficients of equal powers of …

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Mar 2, 2014 · Since coth(x)= 1/tanh(x), we can approximate y= coth(x) near x= 0 with 1/x. Finally, for e^x, the derivative is e^x so both function and derivative are e^0= 1 at x= 0. For small x, y= …

Jul 31, 2014 · If you split at discontinuities, then you use the value at which the discontinuity occurs (of course, provided at least one of either the left or right limits exists and is not infinity). …

Jun 23, 2014 · As the title shows, I want to do they hyperbolic tan of a complex number, using my calculator (casio fx100ms) but I keep getting a maths error, whether I do...

Mar 9, 2025 · Some sources are sloppy about the distinction between the universe and the observable universe (which is the part of the universe we can see, more or less), and also …

Mar 20, 2009 · Hi. How can I derive the Taylor series expansion and the radius of convergence for hyperbolic tangent tanh(x) around the point x=0. I can find the expression for the above in …

Jul 24, 2012 · \tanh{(k)} \approx \pi\ell [/itex] where "l" is very small. What on Earth is the origin of this approximation? I'm sure it's very simple, but I can't seem to derive it from the angle-sum …

May 30, 2011 · Terminal velocity means the velocity at the end of time and time never ends... More precisely terminal velocity is the limit of velocity when the time goes to infinity. It is a …