Curve Sketching again~

Quote:

Originally Posted by ose90

The function f is defined as $f(t)=(4e^kt -1)/(4e^kt +1)$
Find lim f(t) when t tends to infinity and sketch the graph of f.

Thanks, im baffled by the K which is a positive constant.
I found an asymptote on y = 1, and 2 point of intersection.
I can't find any stationary point there as $when f'(t)=0 , 4e^kt + 1 = 0 but 4e^kt + 1 > 0$ therefore no stationary point

You can always substitute a positive value for k to get a feel for things!

$\lim_{t \rightarrow +\infty} \frac{4e^{kt} - 1}{4e^{kt} + 1} = \lim_{t \rightarrow +\infty} \frac{4 - e^{-kt}}{4 + e^{-kt}} = \frac{4 - 0}{4 + 0} = 1$ .

$\lim_{t \rightarrow -\infty} \frac{4e^{kt} - 1}{4e^{kt} + 1} = \lim_{t \rightarrow +\infty} \frac{0 - 1}{0 + 1} = -1$ .

Also, I doubt you've differentiated correctly since the numerator of the derivative is $8 k e^{kt}$ . Even though this still means that there's no stationary point, you should show your working and the answer you obtained so that your mistake can be pointed out.