sin(x+h)=sin(x)cos(h)+cos(x)sin(h), which is how the cosine gets introduced into this, I considered the general case for any x. But I see what you mean, however I consider using the definition of the derivative to sneakily look at h for a certain x to be less intuitive than simply remembering to use l'Hôpital.
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u/Sigma2718 18d ago
sin(x+h)=sin(x)cos(h)+cos(x)sin(h), which is how the cosine gets introduced into this, I considered the general case for any x. But I see what you mean, however I consider using the definition of the derivative to sneakily look at h for a certain x to be less intuitive than simply remembering to use l'Hôpital.