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

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

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limit as x approaches 0 of x*cot(2x)

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

\frac{1}{2}

Decimal Notation

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})

= 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}

\int \frac{9 - 162 x}{1 - 81 x ^{2}} d x

y = a^{5} + cos^{5} (x)

\frac{d}{d x} (\frac{2 x ^{\frac{5}{2}}}{5})

y = x^{2} - 2 x - 3, (2, - 3)

\frac{\partial}{\partial x} (x y)

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