Problem

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

Solution

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 \(\boxed{2}\).

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Source: https://solvelyapp.com/problems/20231/

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