What is the limit as x approaches 0 of (tan^2(x))/(1-cos(x)) ?

The limit as x approaches 0 of (tan^2(x))/(1-cos(x)) is 2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches 0 of (tan^2(x))/(1-cos(x))

x \to 0 lim (\frac{tan ^{2} ( x )}{1 - cos ( x )})

2

Solution steps

x \to 0 lim (\frac{tan ^{2} ( x )}{1 - cos ( x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{2 tan ( x ) sec ^{2} ( x )}{sin ( x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{- 4 sec ^{2} ( x ) + 6 sec ^{4} ( x )}{cos ( x )})

Plug in the value

x = 0

= \frac{- 4 sec ^{2} ( 0 ) + 6 sec ^{4} ( 0 )}{cos ( 0 )}

Simplify

\frac{- 4 sec ^{2} ( 0 ) + 6 sec ^{4} ( 0 )}{cos ( 0 )} : 2

= 2

What is the limit as x approaches 0 of (tan^2(x))/(1-cos(x)) ?
The limit as x approaches 0 of (tan^2(x))/(1-cos(x)) is 2