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})

Plug in the value

x = 0

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

Simplify

= 1

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