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Evaluate the limit.
Lim_(x rarr0)((sin(2x))/(sin(x))).

Evaluate the limit. $\newline$ $\operatorname{Lim}_{x \rightarrow 0} \frac{\sin (2 x)}{\sin (x)}$ .

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Multiplication with rational exponents

Full solution

Q. Evaluate the limit.

\newline

\operatorname{Lim}_{x \rightarrow 0} \frac{\sin (2 x)}{\sin (x)}

.

Apply limit property: Use the limit property that $\lim_{x \to a} f(x) \cdot g(x) = \lim_{x \to a} f(x) \cdot \lim_{x \to a} g(x)$ . So, we can write $\lim_{x \to 0}\left(\frac{\sin(2x)}{\sin(x)}\right)$ as $\lim_{x \to 0}(\sin(2x)) / \lim_{x \to 0}(\sin(x))$ .
Separate limits for $\sin(2x)$ and $\sin(x)$ : Apply the limit to both $\sin(2x)$ and $\sin(x)$ separately. $\newline$ Since $\lim_{x \to 0}(\sin(x)) = 0$ , we get $\lim_{x \to 0}(\sin(2x)) / 0$ .

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