MATLAB: How to make sure that ratios of very large numbers(e^​1000+1)/(e​^1000-1) is not given as NaN

Question

I am trying to plot a function

T = (exp(x) + 1)/(exp(x) - 1)

where x ranges from say -10000 to 10000. Since exp(x) will be very large, the MATLAB is giving NaN instead of actual values. How to overcome this?

Thank you.

Answer 1

You can use an alternate formula for the large values:

T = (1 + 1./exp(x)) ./ (1 - 1./exp(x))

Note that once x gets large enough (19), the ratio calculation becomes equivalent to the "first order" approximation 1 + 2/exp(x) because of the limits of double precision arithmetic.