What is the limit as x approaches 0 of xcot(7/11 x) ?

The limit as x approaches 0 of xcot(7/11 x) is 11/7

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limit as x approaches 0 of xcot(7/11 x)

x \to 0 lim (x cot (\frac{7}{11} x))

\frac{11}{7}

Decimal Notation

1.57142 \dots

Solution steps

x \to 0 lim (x cot (\frac{7}{11} x))

Rewrite for L'Hopital

= x \to 0 lim \frac{x}{\frac{1}{c o t ( \frac{7}{11} x )}}

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{sec ^{2} ( \frac{7 x}{11} ) \frac{7}{11}})

= x \to 0 lim (\frac{1}{sec ^{2} ( \frac{7 x}{11} ) \frac{7}{11}})

Plug in the value

x = 0

= \frac{1}{sec ^{2} ( \frac{7 \cdot 0}{11} ) \frac{7}{11}}

Simplify

\frac{1}{sec ^{2} ( \frac{7 \cdot 0}{11} ) \frac{7}{11}} : \frac{11}{7}

= \frac{11}{7}

\int_{1}^{e} x^{2} ln (x) d x

\frac{d y}{d x} = (x y^{2})

x \to 0 lim (\frac{3 x}{tan ( x )})

y^{^{'}} - 2 x y = 2 x

x \to 1 lim (arctan (x))

What is the limit as x approaches 0 of xcot(7/11 x) ?
The limit as x approaches 0 of xcot(7/11 x) is 11/7