What is the limit as x approaches 0 of xcot(3/5 x) ?

The limit as x approaches 0 of xcot(3/5 x) is 5/3

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limit as x approaches 0 of xcot(3/5 x)

x \to 0 lim (x cot (\frac{3}{5} x))

\frac{5}{3}

Decimal

1.66666 \dots

Solution steps

x \to 0 lim (x cot (\frac{3}{5} x))

Rewrite for L'Hopital

= x \to 0 lim \frac{x}{\frac{1}{c o t ( \frac{3}{5} x )}}

Apply L'Hopital's Rule

= x \to 0 lim (\frac{1}{sec ^{2} ( \frac{3 x}{5} ) \frac{3}{5}})

Plug in the value

x = 0

= \frac{1}{sec ^{2} ( \frac{3 \cdot 0}{5} ) \frac{3}{5}}

Simplify

\frac{1}{sec ^{2} ( \frac{3 \cdot 0}{5} ) \frac{3}{5}} : \frac{5}{3}

= \frac{5}{3}

What is the limit as x approaches 0 of xcot(3/5 x) ?
The limit as x approaches 0 of xcot(3/5 x) is 5/3