Vault Of Euclid

Limit of (x + sin 2x) / (x - sin x) as x approaches 0

Limits warmup

\(\lim_{x\to 0} \frac{x + \sin 2x}{x - \sin x}\)

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What you need first

Evaluating limits by direct substitution
L'Hôpital's rule
Derivatives of trigonometric functions
The chain rule

What this problem tests

Tests the ability to apply L'Hôpital's rule and correctly interpret a non-zero divided by zero result.

This is a standard calculus problem demonstrating that L'Hôpital's rule can lead to a non-existent limit.

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