We judge the existence of e by judging the limit of sequence. First, we judge that the sequence x _ n = (1+ 1/n) n is an increasing sequence.

Then it is proved that x_n has an upper bound.

04 The second limit is about the situation that sin(x), x and tan(x) of the arc of the curve are replaced by straight lines, and they approach 0 in x..

So there is the following inequality. On this basis, the limit of x/sinx when x tends to 0 is deduced.

Similarly, the limit value of x/tanx is as follows.