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

Vault Of Euclid

Limit of tan(x)/x as x approaches 0

Limits warmup

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

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
Evaluating 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, including knowing the derivative of the tangent function.

This is a standard introductory calculus problem demonstrating the application of L'Hôpital's rule to trigonometric limits.

Limit of tan(x)/x as x approaches 0

What you need first

What this problem tests

More on Limits