If $$\lim_{x \to a} g(x) = b$$ and $$f$$ is continuous at $$b$$:
$$\lim_{x \to a} f(g(x)) = f\left(\lim_{x \to a} g(x)\right) = f(b)$$
Requires continuity of $$f$$ at the limit point.
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CAT Formulas
Limits
Limits of Composite Functions
If $$\lim_{x \to a} g(x) = b$$ and $$f$$ is continuous at $$b$$:
$$\lim_{x \to a} f(g(x)) = f\left(\lim_{x \to a} g(x)\right) = f(b)$$
Requires continuity of $$f$$ at the limit point.
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