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

The limit as x approaches 0 of xarctan(x) is 0

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limit as x approaches 0 of xarctan(x)

x \to 0 lim (x arctan (x))

0

Solution steps

x \to 0 lim (x arctan (x))

Plug in the value

x = 0

= 0 \cdot arctan (0)

Simplify

0 \cdot arctan (0) : 0

= 0

x \to 3 lim ((3 x) (4 x))

x \to \frac{π}{2} lim (arctan (x))

h \to 0 lim (3 x^{2} + 3 x h + h^{2})

x \to 0 + lim (\frac{x}{ln ( x + 1 )})

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

What is the limit as x approaches 0 of xarctan(x) ?
The limit as x approaches 0 of xarctan(x) is 0