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) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

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

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

= 0

\int (2 x^{3} + 3 x + 1)^{4} (6 x^{2} + 3) d x

\int \frac{1}{x ( 1 + x ^{2} )} d x

(ln (1 - x^{2}))^{^{'}}

\frac{d}{d x} (cos (y x^{2} + 1))

x y^{2} y^{^{'}} = y^{3} - 2 x^{3}

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