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

\frac{4}{1 + x ^{2}}

f (x) = cos (x) - x sin (x)

\frac{d}{d x} (e^{x} (x^{2} - 3 x + 1))

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

f (t) = \frac{8}{t ^{2}}, at t = 1

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