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The value of $\lim_{x \to 0} \frac{x - \tan(3x)}{\sin(2x)}$ is equal to
The value of $\lim_{x \to 0} \frac{x - \tan(3x)}{\sin(2x)}$ is equal to
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Alternatively, divide terms by $x$: $\lim \frac{1 - 3\frac{\tan 3x}{3x}}{2\frac{\sin 2x}{2x}} = \frac{1 - 3(1)}{2(1)} = -1$. Standard limits are often faster than differentiation!
Updated On: Jun 24, 2026
- $-\frac{3}{2}$
- $\frac{2}{3}$
- -2
- 1
- -1
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