Evaluate the fundamental trigonometric limit of sin(x)/x as x approaches 0 using L'Hôpital's rule.

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Evaluating the Limit of sin(x)/x as x Approaches 0

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\[ \lim_{x\to 0} \frac{\sin x}{x} \]

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What you need first

L'Hôpital's rule
Derivative of the sine function
Evaluating limits by direct substitution
Values of trigonometric functions at zero

What this problem tests

Tests the ability to recognize a 0/0 indeterminate form and correctly apply L'Hôpital's rule by differentiating the numerator and denominator.

This is one of the most famous limits in early calculus. While usually proven geometrically to establish the derivatives of trigonometric functions, it is often revisited later as a straightforward application of L'Hôpital's rule.

Evaluating the Limit of sin(x)/x as x Approaches 0

What you need first

What this problem tests

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