Theorem

Suppose that f(x) → 0 and g(x) → 0 as x → a. Then

if the limit on the right‐hand side exists.

For example,

The result also holds if f(x) → ∞ and g(x) → ∞ as x → a. Moreover, the rule applies if ‘x → a' is replaced by ‘x →+∞' or ‘x →−∞'.

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