けんき says to YSITD
we have for all e>0 we have d>0 and k=min(all possible |f(x)*f(a)| for current e) such that 0<|x-a|<d then |f(x)-f(a)|<e*k we know |1/f(x)-1/f(a)|=|f(a)-f(x)|/|f(x)f(a)| we can get the following formula from |f(x)-f(a)|<e*k : |f(a)-f(x)|/|f(x)f(a)|<e*k/|f(x)*f(a)|<e