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up vote 5 down vote favorite Consider $$lim_{xtoinfty}frac{f(x)}{g(x)} + lim_{xtoinfty}frac{h(x)}{i(x)}$$ I was told that I cannot apply L'Hôpital's rule to each individual limit and then join the limits as $$lim_{xtoinfty}frac{f(x)}{g(x)} +frac{h(x)}{i(x)}$$ Why is this incorrect? calculus limits share | cite | improve this question edited Nov 29 at 4:27 snorepion 3 1 asked Nov 29 at 0:16 Danielle 181 9