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

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

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

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