lim sinx/x khi x tiến tới 0

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Lim of sin(x)/x as x goes to tướng zero

Learning this and trying to tướng remember it by understanding the proof that shows the answer is one. When I try to tướng apply the product rule I get confused. Product rule says lim as x=> 0 of sin(x)/x should equal limit sin(x) * limit (1/x). One of these factors goes to tướng zero and the other goes to tướng infinity, yet the answer is one. I have a hard time wrapping my head around this.