Why Special Limit of Euler's Number fails at higher powers? In the "Calculus 6th edition" by Edwards and Penney, in the chapter of Transcendental functions, there is an interesting question about special limit that leads to the famous Euler's number 2.718281828. It is given as:
$$\lim_{x\to\infty}(1+ \frac{1}x)^x$$ 
However, if you rise variable x to the higher power, say 10:
the graph literally goes crazy  as x goes to infinity, and the kills of to 1. Here is the graph of this situation:

This special limit states that: the further you go with x the closer you approach e. So, as you see the limit fails at higher powers. Please, help me to to understand this situation. I suppose it has something to do with the capability of computer systems to calculate. 
Thank you!

The flat part of the graph is an error caused by underflow. To the computer, $10^{-10}=0$, so you have $(1+0)^{10^{10}}$.
The crazy part is probably caused by floating point error.
In short, both of these problems are probably caused by the finite precision allowed by computers.
