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

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

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limit as x approaches 0 of x*cot(3x)

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

\frac{1}{3}

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})

= 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}

x \to - \infty lim (1 - x)

x \to 0 + lim ((\frac{x}{x + 1})^{x})

x \to 0 lim (\frac{9 x ^{4}}{5 x ^{4}} - 12)

n \to \infty lim (\frac{ln ( \frac{1}{n} )}{2 n})

x \to π + lim (cos (x))

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