What is the limit as x approaches 0 of (1-cos(4x))/(xtan(3x)) ?

The limit as x approaches 0 of (1-cos(4x))/(xtan(3x)) is 8/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 0 of (1-cos(4x))/(xtan(3x))

x \to 0 lim (\frac{1 - cos ( 4 x )}{x tan ( 3 x )})

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

x \to 0 lim (\frac{1 - cos ( 4 x )}{x tan ( 3 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{4 sin ( 4 x )}{tan ( 3 x ) + 3 x sec ^{2} ( 3 x )})

= x \to 0 lim (\frac{4 sin ( 4 x )}{tan ( 3 x ) + 3 x sec ^{2} ( 3 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{16 cos ( 4 x )}{6 sec ^{2} ( 3 x ) + 18 x sec ^{2} ( 3 x ) tan ( 3 x )})

= x \to 0 lim (\frac{16 cos ( 4 x )}{6 sec ^{2} ( 3 x ) + 18 x sec ^{2} ( 3 x ) tan ( 3 x )})

Plug in the value

x = 0

= \frac{16 cos ( 4 \cdot 0 )}{6 sec ^{2} ( 3 \cdot 0 ) + 18 \cdot 0 \cdot sec ^{2} ( 3 \cdot 0 ) tan ( 3 \cdot 0 )}

Simplify

\frac{16 cos ( 4 \cdot 0 )}{6 sec ^{2} ( 3 \cdot 0 ) + 18 \cdot 0 \cdot sec ^{2} ( 3 \cdot 0 ) tan ( 3 \cdot 0 )} : \frac{8}{3}

= \frac{8}{3}

\frac{\partial}{\partial x} (- 2 e^{- 7 x y})

\int - \frac{1}{cos ( x )} d x

\frac{d}{d x} (\frac{3}{6 - x})

\frac{d}{d x} (3 x^{4} + 15)

e^{6 x} cos (9 x)

What is the limit as x approaches 0 of (1-cos(4x))/(xtan(3x)) ?
The limit as x approaches 0 of (1-cos(4x))/(xtan(3x)) is 8/3