When x tends to infinity, sinx and cosx have no limit.
Assuming that the sinx limit exists, then according to the definition of infinite limit,
Find a number X0 so that a small enough number e is equal to all x >；; X0 hours
/sinx-sinX0/
=(sinx-x)/x/(cosx-x)/x (numerator and denominator divided by x)
=(_ sinx/x- 1)/(cosx/x- 1)
=2sinX0
=0
The method of finding the limit of sequence by expanding data;
Let the unary real function f(x) be defined in the eccentric neighborhood of point x0. If the function f(x) has one of the following conditions:
1, the function f(x) exists at the left and right limits of point x0, but it is not equal, that is, f(x0+)≠f(x0-).
2. At least one function f(x) does not exist in the left and right limits of point x0.
3. The left and right limits of function f(x) exist and are equal at point x0, but it does not mean that f(x0) or f(x) is undefined at point x0.
Then the function f(x) is discontinuous at point x0, which is called the discontinuous point of the function f(x).