What is the limit as x approaches 0 of xcot(2x) ?

The limit as x approaches 0 of xcot(2x) is 1/2

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 xcot(2x)

x \to 0 lim (x cot (2 x))

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to 0 lim (x cot (2 x))

Rewrite for L'Hopital

= x \to 0 lim (\frac{x}{\frac{1}{c o t ( 2 x )}})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{sec ^{2} ( 2 x ) \cdot 2})

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

Plug in the value

x = 0

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

sec^{2} (2 \cdot 0) \cdot 2 = 2

= \frac{1}{2}

\int_{0}^{25} \frac{4}{5} x d x

y^{^{'}} + y = 5 \cdot x + 1

\frac{\partial}{\partial z} (x y^{2} z)

y^{^{''}} + 8 y^{^{'}} + 4 y = 0

f (x) = \frac{x ^{2}}{x ^{2} + 7}

What is the limit as x approaches 0 of xcot(2x) ?
The limit as x approaches 0 of xcot(2x) is 1/2