What is the limit as x approaches 0 of 2arctan(x) ?

The limit as x approaches 0 of 2arctan(x) is 0

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limit as x approaches 0 of 2arctan(x)

x \to 0 lim (2 arctan (x))

0

Solution steps

x \to 0 lim (2 arctan (x))

Plug in the value

x = 0

= 2 arctan (0)

Simplify

2 arctan (0) : 0

= 0

x \to 0 + lim (\frac{( x cos ( x ) )}{2 x})

x \to 0 lim (3 \frac{x}{cos ( x )})

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

x \to 0 lim (\frac{3 x ^{2} + 5 cos ( x ) - 5}{2 x})

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

What is the limit as x approaches 0 of 2arctan(x) ?
The limit as x approaches 0 of 2arctan(x) is 0