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 (cot (2 x)))

\frac{1}{2}

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}

x, x^{2}

\frac{d}{d x} (1 + x^{3})

f (x) = 5 x + 6, at x = 2

x \frac{d y}{d x} + 2 y = 8 x^{2}

n = 0 \sum \infty \frac{5}{4 ^{n}}

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