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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I'm confused. If f(x) = sin(x), f'(x) exists everywhere, but has no well defined limit at infinity
Right but sin(x) doesn’t have a derivative at infinity, so it doesn’t meet the hypothesis
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O I see. The condition is that f'(x) must converge at infinity. So I can picture that statement geometrically as the slope of a large triangle with base x and height f(x) approximating the final slope of f(x) at infinity.
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