What is the limit as t approaches 0 of (tan(3t))/t ?

The limit as t approaches 0 of (tan(3t))/t is 3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as t approaches 0 of (tan(3t))/t

t \to 0 lim (\frac{tan ( 3 t )}{t})

3

Solution steps

t \to 0 lim (\frac{tan ( 3 t )}{t})

Apply L'Hopital's Rule

= t \to 0 lim (\frac{sec ^{2} ( 3 t ) \cdot 3}{1})

Plug in the value

t = 0

= \frac{sec ^{2} ( 3 \cdot 0 ) \cdot 3}{1}

Simplify

\frac{sec ^{2} ( 3 \cdot 0 ) \cdot 3}{1} : 3

= 3

What is the limit as t approaches 0 of (tan(3t))/t ?
The limit as t approaches 0 of (tan(3t))/t is 3