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

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

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limit as x approaches 0 of xcot(2x)

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

\frac{1}{2}

Decimal

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})

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}

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