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The value of $\lim_{x\rightarrow 0}\frac{\sqrt{1+3x}-\sqrt{1-3x}}{x}$ is
The value of $\lim_{x\rightarrow 0}\frac{\sqrt{1+3x}-\sqrt{1-3x}}{x}$ is
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Logic Tip: You can also use L'Hôpital's rule. The derivative of $\sqrt{1 \pm 3x}$ is $\frac{\pm 3}{2\sqrt{1 \pm 3x}}$. Applying this to the numerator gives $\frac{3}{2(1)} - \frac{-3}{2(1)} = \frac{3}{2} + \frac{3}{2} = 3$. The denominator derivative is 1. This provides the answer immediately!
Updated On: Apr 27, 2026
- 0
- 1
- $\frac{1}{3}$
- $\frac{1}{2}$
- 3
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The Correct Option is
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