Question

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

Answer 1

see below

Explanation:

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`