What is the limit as x approaches 0 of 3arctan(e^x) ?

The limit as x approaches 0 of 3arctan(e^x) is 3*pi/4

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limit as x approaches 0 of 3arctan(e^x)

x \to 0 lim (3 arctan (e^{x}))

3 \cdot \frac{π}{4}

Solution steps

x \to 0 lim (3 arctan (e^{x}))

Plug in the value

x = 0

= 3 arctan (e^{0})

Simplify

3 arctan (e^{0}) : 3 \cdot \frac{π}{4}

= 3 \cdot \frac{π}{4}

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What is the limit as x approaches 0 of 3arctan(e^x) ?
The limit as x approaches 0 of 3arctan(e^x) is 3*pi/4