Question: How can I detect a possible discontinuity using a plot in Maple?

Good day.

I am looking into the behaviour of a function, V, that depends on several parameter values; these values are fixed in the attached example. However, I have encountered an issue that is puzzling me and I was hoping that someone may be able to shine a light on this for me.

Basically,  I would like to understand how the solution, V, behaves as the value of exponent, beta, approaches infinity.

Straightforward analysis suggests that the value of V tends to -10 as beta grows infinitely large (s -> C, and beta ->infinity and so, V -> -10 ... so far, so good).

However, when the function is plotted, the solution seems to converge to a value, 6.5, as beta tends to a very large number (10^17).

Now .. here's the mystery .. there appears to be a critical value of around 7.854 x 10^17; here, the limit seems to switch from V=6.5 to -10. Does this phenomenon correspond to a discontinuity or is it related to the computational process? Are there any built-in routines in Maple to check for such potential conditions?

Thanks for reading!

MaplePrimes_Sep_19.mw