what is the asymptote of y=sinhx?

Answer 1

No asymptote. It just keeps growing. That is, as x─►±∞, y ─►±∞.

Answer 2

I didn't think that y=sin x had an asymptote.
An asymptote is a straight line on a graph where the curve doesn't quite reach. For example the function y=1/x has a vertical asymptote at x=0 and a horizontal asymptote at y=0.
I may be wrong but as far as I know sin and cos curves do not have asymptotes. Tan curves however, do.

Answer 3

y= sinh x has no asymptotes per se, this is easily seen from the definition of the hyperbolic sine, i.e,

sinh x = (e^x - e^-x) / 2
Now all's well for positive values of x and 0
(at which sinh 0 = (1-1)/2 = 0)
Now consider negative values of x, then e^x is small but non negative, yet e^(-x) is large and owing to the negative sign negative. Therefore it will yield a negative quantity.
Note how even upon rearranging as,
[e^2x - 1] / [2e^x]
the denominator will never be zero for observable values of x (excluding infinity that is)

Hope this helps!!
PS- for pure imaginary z in sinh z the function becomes
sin [Im{z}] , for complex quantities some manipulation becomes necessary.

Answer 4

y'=1divided by
sqrt of 1+xsquare

Answer 5

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