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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{1}{\frac{1}{0 ^{2} + 1}}

Simplify

= 1

\int_{- 1}^{1} 3 e^{- 3 x} d x

5 e^{- 2 t}

y^{^{'}} = 12 t^{5} - 20 t^{4} + 2 - 6 t^{- 2}

y = t e^{- 3 t} sin (5 t)

\frac{( 3 x - 7 )}{( 9 x + 5 )} + x^{3}

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