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

The limit as x approaches 0 of x/(arctan(11x)) is 1/11

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limit as x approaches 0 of x/(arctan(11x))

x \to 0 lim (\frac{x}{arctan ( 11 x )})

\frac{1}{11}

Decimal

0.09090 \dots

Solution steps

x \to 0 lim (\frac{x}{arctan ( 11 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{\frac{11}{121 x ^{2} + 1}})

= x \to 0 lim (\frac{1}{\frac{11}{121 x ^{2} + 1}})

Plug in the value

x = 0

= \frac{1}{\frac{11}{121 \cdot 0 ^{2} + 1}}

Simplify

= \frac{1}{11}

\int (x + 3)^{2} d x

\frac{d y}{d t} = 3 y - e^{3 t} + 6 t^{2} - 2

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 2 x y + y ^{2}})

\frac{d}{d x} ((4 x - 8)^{2})

\int_{0}^{x} 3 e^{- 3 x} d x

What is the limit as x approaches 0 of x/(arctan(11x)) ?
The limit as x approaches 0 of x/(arctan(11x)) is 1/11