The Hidden Paradox in Using L’Hôpital on sin(x)/x скачать в хорошем качестве

The Hidden Paradox in Using L’Hôpital on sin(x)/x

Showing why L'Hopital's rule cannot be used for the limit sinx/x as x tends to zero, because of the cyclic nature of this problem. To know that the derivative of sin(x)=cos(x) we need to know that the limit as x goes to zero of sin(x)/x=1. Edit: I am assuming we do not yet know what the derivative of sin(x) is...there are other ways to show that the derivative of sin(x)=cos(x), if you have already shown it, then Lhopital can be used. However if we have already shown that the derivative of sinx=cosx, then we have also shown that the limit of six/x as x goes to zero =1, because of how the limit is connected to the derivative as shown in the video. So by saying we need to show/prove sinx/x=1 as x tends to 0, we are automatically saying we do not yet know what the derivative of sinx is.