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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

= 1

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

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

\int \frac{5 x + 4}{( x + 8 ) ^{2} ( x - 1 )} d x

\frac{s ^{2} + 9}{s ( s + 4 )}

\frac{d y}{d x} = \frac{x - 1}{x + 3} \frac{y - 2}{y - 3}

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