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

x \to 1 lim (\frac{x ^{2} - 1}{x + 3})

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

x \to 0 + lim (\frac{x}{e ^{- \frac{6}{x}}})

x \to \frac{1}{2} lim (2 x + 4)

x \to 4 lim (\frac{x - 2}{x ^{2} - 4})

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