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

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

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limit as x approaches 0 of xcot(4x)

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

\frac{1}{4}

Decimal

0.25

Solution steps

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

Rewrite for L'Hopital

= 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})

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

Plug in the value

x = 0

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

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

= \frac{1}{4}

x \to \infty lim (6 x + 3)

x \to 1 lim (3 x - 8)

x \to 2 a lim (2 a - 3 x)

x \to 1 - lim (\frac{x - 1}{x - 1})

x \to 8 lim (96)

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