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

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

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limit as x approaches 0+of xarctan(1/x)

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

0

Solution steps

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to 0 + lim (x) \cdot x \to 0 + lim (arctan (\frac{1}{x}))

x \to 0 + lim (x) = 0

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

= 0 \cdot \frac{π}{2}

Simplify

= 0

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