I'm confused. If f(x) = sin(x), f'(x) exists everywhere, but has no well defined limit at infinity
Suppose that f'(x) exists on some interval (a, ∞) where a ∈ ℝ. Then, the following equality holds.pic.twitter.com/Vdoh9JMOkh
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Right but sin(x) doesn’t have a derivative at infinity, so it doesn’t meet the hypothesis
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L'Hôpital's rule
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a "weaker" version of L'Hopital's rule (at once wider and more constrained - you don't need infinity/infinity but you can only have x on the bottom rather than any function that goes to infinity)
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This is similar to L'Hospital with one exception: f(x)'s limit at infinity is not given as infinity..
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