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

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

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limit as x approaches 0 of 2xcot(x)

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

2

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Rewrite for L'Hopital

= 2 \cdot x \to 0 lim (\frac{x}{\frac{1}{c o t ( x )}})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{sec ^{2} ( x )})

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

Plug in the value

x = 0

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

Simplify

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

= 2

\frac{d}{d x} (\frac{( 2 x + x ^{2} )}{( 1 + x ) ^{2}})

\frac{d y}{d x} = y^{2} (1 + x^{2})

ln (3 - 2 x)

\int (\frac{x ^{2} + 9}{x ^{3}}) d x

3 cos^{3} (5 x)

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