How do you prove that the triad of graphs of $y = cosh x, y = sinh x$ $y = cosh x , y = sinh x$ and ( their bisector in the y-direction ) $y = (\frac{1}{2}) e^{x}$ $y =(1/2) e^x$ becomes asymptotic, as $x \to \infty$ $x to oo$ ?

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Answer 1 · 2016-08-29T12:22:32

see below

I may have misunderstood the question but is it not a case of something like this for sinh and cosh:

$lim_(x to oo) (e^x pm e^-x)/2$

$=lim_(x to oo) 1/2e^x pm lim_(x to oo) 1/2 e^-x$

$=lim_(x to oo) 1/2e^x pm 0$

$=lim_(x to oo) 1/2e^x$

How do you prove that the triad of graphs of y = cosh x , y = sinh xy=coshx,y=sinhxy = cosh x , y = sinh x and ( their bisector in the y-direction ) y =(1/2) e^xy=(12)exy =(1/2) e^x becomes asymptotic, as x to oox→∞x to oo?