What is the limit as x approaches 0 of xcot(10/3 x) ?

The limit as x approaches 0 of xcot(10/3 x) is 3/10

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limit as x approaches 0 of xcot(10/3 x)

x \to 0 lim (x cot (\frac{10}{3} x))

\frac{3}{10}

Decimal

0.3

Solution steps

x \to 0 lim (x cot (\frac{10}{3} x))

Rewrite for L'Hopital

= x \to 0 lim \frac{x}{\frac{1}{c o t ( \frac{10}{3} x )}}

Apply L'Hopital's Rule

= x \to 0 lim (\frac{1}{sec ^{2} ( \frac{10 x}{3} ) \frac{10}{3}})

Plug in the value

x = 0

= \frac{1}{sec ^{2} ( \frac{10 \cdot 0}{3} ) \frac{10}{3}}

Simplify

\frac{1}{sec ^{2} ( \frac{10 \cdot 0}{3} ) \frac{10}{3}} : \frac{3}{10}

= \frac{3}{10}

d er i v a t i v e y = x^{2} 8 x - 9

y^{^{''}} + 4 y = sec^{3} (2 x)

t an g e n t y = arctan (- x), at x = 3

\int 2 - x^{2} d x

\frac{d}{d x} (\frac{2}{tan ( x )})

What is the limit as x approaches 0 of xcot(10/3 x) ?
The limit as x approaches 0 of xcot(10/3 x) is 3/10