What is the limit as x approaches 0 of xcot(5x) ?

The limit as x approaches 0 of xcot(5x) is 1/5

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limit as x approaches 0 of xcot(5x)

x \to 0 lim (x cot (5 x))

\frac{1}{5}

Decimal

0.2

Solution steps

x \to 0 lim (x cot (5 x))

Rewrite for L'Hopital

= x \to 0 lim (\frac{x}{\frac{1}{c o t ( 5 x )}})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{sec ^{2} ( 5 x ) \cdot 5})

= x \to 0 lim (\frac{1}{sec ^{2} ( 5 x ) \cdot 5})

Plug in the value

x = 0

= \frac{1}{sec ^{2} ( 5 \cdot 0 ) \cdot 5}

sec^{2} (5 \cdot 0) \cdot 5 = 5

= \frac{1}{5}

\int (2 x - 5) (x - 3)^{9} d x

(y^{2} + 16) d x - (\frac{1}{( 3 x + 5 ) ^{2}}) d y = 0

\int \frac{12}{12 + e ^{x}} d x

\frac{t}{t + 1}

\int cot^{3} (11 x) d x

What is the limit as x approaches 0 of xcot(5x) ?
The limit as x approaches 0 of xcot(5x) is 1/5