Vault Of Euclid

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

Trigonometric and inverse trigonometric functions warmup

Evaluate \( \lim_{x\to 0} \frac{\tan x}{x} \).

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

What you need first

the definition of the tangent function in terms of sine and cosine
the fundamental limit of sin(x)/x as x approaches 0
the limit product rule
the value of cos(0)

What this problem tests

Tests the ability to rewrite trigonometric expressions to reveal known limits and apply basic limit laws.

This is a standard introductory calculus problem that reinforces the use of the fundamental limit of sin(x)/x.

More on Trigonometric and inverse trigonometric functions

Tangent Line to Sine Squared warmup
Derivative of Cosine Squared warmup
Integral Yielding an Arcsine Function warmup
Horizontal Tangents of the Secant Function warmup
Derivative of 2 tan(x/2) - 5 warmup
Derivative of x^2 cos(2x) warmup

← today's set