Evaluate the following limit:
\[
\lim _{x \rightarrow 0} \frac{2 \sin (x)}{x}
\]
a. 2
b. 1
c. 0
d. $\pi$

Answer

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Answer

The limit of the given expression as $x$ approaches 0 is $\boxed{2}$.

Steps

Step 1 ：The limit is of the form $\frac{0}{0}$ as $x$ approaches 0. This is an indeterminate form.

Step 2 ：However, we know that $\lim_{x \rightarrow 0} \frac{\sin(x)}{x} = 1$ from the standard limit results.

Step 3 ：Therefore, we can use this result to find the limit of the given expression.

Step 4 ：The limit of the given expression as $x$ approaches 0 is $\boxed{2}$.