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

The limit as x approaches 0 of x/(2tan(x)) 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 x/(2tan(x))

x \to 0 lim (\frac{x}{2 tan ( x )})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to 0 lim (\frac{x}{2 tan ( x )})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Use the basic trigonometric identity:

\frac{1}{tan ( x )} = cot (x)

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

Rewrite for L'Hopital

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= \frac{1}{2}

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

\int_{0}^{1} \frac{1}{5 x - 3} d x

2 y^{^{''}} + y^{^{'}} - y = x + 1

x \to 3 lim (x^{2} + 4 x - 3)

\frac{d}{d x} (x^{3} - 4)

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