What is the limit as x approaches 0 of 2xcot(4x) ?

The limit as x approaches 0 of 2xcot(4x) is 1/2

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limit as x approaches 0 of 2xcot(4x)

x \to 0 lim (2 x cot (4 x))

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to 0 lim (2 x cot (4 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 (4 x))

Rewrite for L'Hopital

= 2 \cdot x \to 0 lim (\frac{x}{\frac{1}{c o t ( 4 x )}})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{sec ^{2} ( 4 x ) \cdot 4})

= 2 \cdot x \to 0 lim (\frac{1}{sec ^{2} ( 4 x ) \cdot 4})

Plug in the value

x = 0

= 2 \cdot \frac{1}{sec ^{2} ( 4 \cdot 0 ) \cdot 4}

Simplify

2 \cdot \frac{1}{sec ^{2} ( 4 \cdot 0 ) \cdot 4} : \frac{1}{2}

= \frac{1}{2}

y = \frac{6 x}{x + 2}

e^{- t}

\int \frac{1}{u ^{3}} d u

\frac{\partial}{\partial x} (x^{7} + 3^{y} + x^{y})

\frac{d}{d y} (- ln (y))

What is the limit as x approaches 0 of 2xcot(4x) ?
The limit as x approaches 0 of 2xcot(4x) is 1/2