Suppose $L=\lim_{x\to0^+}f(x)=\lim_{x\to0^+}g(x)$, where $L$ is finite. Can I calculate $$\lim_{x\to0^+}\frac{L-f(x)}{L-g(x)}$$ without knowing either $f'(x)$ or $g'(x)$?
2026-03-25 09:35:01.1774431301
Value of a limit inside another limit
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No we can't since we don't know the rate for $f(x)$ and $g(x)$ to tend at L (that is just the information we can have by derivatives).
Let for example
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