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

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

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limit as x approaches 0-of x*arctan(1/x)

x \to 0 - lim (x \cdot 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

\frac{d y}{d x} = \frac{2 x}{1 + 2 y}, y (2) = 0

n = 1 \sum \infty (- 1)^{n - 1} \frac{2 ^{n}}{n ^{4}}

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

\int \frac{sin ( 5 x )}{16 + cos ^{2} ( 5 x )} d x

\frac{\partial}{\partial x} (6 x + 5 y)

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