2016年5月5日 · Use formula: coshx = ex + e−x 2 and sinhx = ex −e−x 2 Right side: = cosh2x +sinh2x = (ex +e−x 2)2 + (ex − e−x 2)2 = e2x + 2 + e−2x 4 + e2x −2 +e−2x ...

2015年11月7日 · cosh(z) = ez + e−z 2 So: cosh(ln(x)) = eln(x) +e−ln(x) 2 = x + 1 x 2 = x2 + 1 2x

2018年4月16日 · How do you find the power series for f (x) = cosh(x2) and determine its radius of convergence?

2018年3月6日 · See the proof below I am going to prove the following cosh2x=2cosh^2x-1 By the definition of hyperbolic functions cosh (2x)= (e^ (2x)+e^ (-2x))/2 coshx= (e^x+e^-x ...

2017年7月24日 · Well, I don't work with hyperbolics much, but I do know that: the derivative of tanh (x) is still sech^2 (x). we still have cosh (x) = 1/ (sech (x)). we however, have that -sinh^2 …

2017年3月5日 · = 1/2 x sqrt (x^2 - 1) - 1/2 cosh^ (-1) (x) + C When you say you want the "anti-derivative" of int sqrt (x^2-1) dx, I am assuming you mean you want the "anti-derivative" that is …

2016年5月4日 · see below Let y=cosh^-1x then by definition x=cosh y =(e^y+e^-y)/2 2x=e^y+e^-y e^y-2x+e^-y=0 e^y-2x+1/e^y=0 e^(2y)-2xe^y+1=0 Let u=e^y then we have u^2-2xu+1=0--> …

2017年10月15日 · See explanation... >cosh x = 1/2 (e^x+e^ (-x)) sinh x = 1/2 (e^x-e^ (-x)) So: cosh^2 x - sinh^2 x = 1/4 ( (e^x+e^ (-x))^2- (e^x-e^ (-x))^2) color (white) (cosh^2 x ...

2018年5月12日 · show below cosh(x +y) = cosh(x) ⋅ cosh(y) +sinh(x) ⋅ sinh(y) R.H.S = cosh(x) ⋅ cosh(y) + sinh(x) ⋅ sinh(y) = [ex +e−x 2] ⋅ [ey + e−y 2] + [ex − e−x ...

2016年5月3日 · See below Use the definition of Hyperbolic Functions for cosh x cosh x = (e^x + e^-x)/2 and sinh x= (e^x-e^-x)/2 cosh (A+B)=coshAcoshB+sinhAsinhB Right Side: = [ (e^A ...