What is the limit as x approaches 0 of xcot(3x) ?

The limit as x approaches 0 of xcot(3x) is 1/3

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limit as x approaches 0 of xcot(3x)

x \to 0 lim (x cot (3 x))

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

x \to 0 lim (x cot (3 x))

Rewrite for L'Hopital

= x \to 0 lim (\frac{x}{\frac{1}{c o t ( 3 x )}})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{1}{sec ^{2} ( 3 x ) \cdot 3})

Plug in the value

x = 0

= \frac{1}{sec ^{2} ( 3 \cdot 0 ) \cdot 3}

sec^{2} (3 \cdot 0) \cdot 3 = 3

= \frac{1}{3}

What is the limit as x approaches 0 of xcot(3x) ?
The limit as x approaches 0 of xcot(3x) is 1/3