Evaluate a fundamental trigonometric limit using L'Hôpital's rule.

Vault Of Euclid

Limit of (1 - cos x)/x as x approaches 0

Limits warmup

\(\lim_{x\to 0} \frac{1 - \cos x}{x}\)

The solution and a full step-by-step explanation are here. Sign in to read them.

What you need first

Evaluating limits by direct substitution
Recognizing indeterminate forms
L'Hôpital's rule
Derivatives of basic trigonometric functions

What this problem tests

Tests the ability to recognize a 0/0 indeterminate form and correctly apply L'Hôpital's rule to trigonometric functions.

This is a fundamental limit often encountered early in a Calculus I course, both as an exercise in L'Hôpital's rule and as a lemma for finding the derivative of sine and cosine from first principles.

Limit of (1 - cos x)/x as x approaches 0

What you need first

What this problem tests

More on Limits