What is the limit as x approaches 0 of x/(arctan(6x)) ?

The limit as x approaches 0 of x/(arctan(6x)) is 1/6

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limit as x approaches 0 of x/(arctan(6x))

x \to 0 lim (\frac{x}{arctan ( 6 x )})

\frac{1}{6}

Decimal Notation

0.16666 \dots

Solution steps

x \to 0 lim (\frac{x}{arctan ( 6 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{\frac{6}{36 x ^{2} + 1}})

= x \to 0 lim (\frac{1}{\frac{6}{36 x ^{2} + 1}})

Plug in the value

x = 0

= \frac{1}{\frac{6}{36 \cdot 0 ^{2} + 1}}

Simplify

= \frac{1}{6}

x \to 0 + lim (x^{2} + 3 x - 4)

\frac{d}{d x} (\frac{10}{1 + e ^{- x}})

\frac{d y}{d x} + (\frac{1}{200 + 3 x}) y = 8

- 4 x y^{4} = \frac{d y}{d x}

\frac{d}{d t} (a cos (t), b sin (t), t)

What is the limit as x approaches 0 of x/(arctan(6x)) ?
The limit as x approaches 0 of x/(arctan(6x)) is 1/6