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Find the limit as x approaches 0 of sin(x)/x

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Answer
1\boxed{1}

This is a fundamental trigonometric limit that can also be verified using L'Hôpital's Rule by differentiating the numerator and denominator.

Problem: Find the limit lim⁡x→0sin⁡(x)x\lim_{x \to 0} \frac{\sin(x)}{x}.

Steps

  1. Recognize a standard limit
    lim⁡x→0sin⁡(x)x=1\lim_{x \to 0} \frac{\sin(x)}{x} = 1

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