What is the limit as x approaches 0 of (1+2x)^x ?

The limit as x approaches 0 of (1+2x)^x is 1

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limit as x approaches 0 of (1+2x)^x

x \to 0 lim ((1 + 2 x)^{x})

1

Solution steps

x \to 0 lim ((1 + 2 x)^{x})

Plug in the value

x = 0

= (1 + 2 \cdot 0)^{0}

Simplify

= 1

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What is the limit as x approaches 0 of (1+2x)^x ?
The limit as x approaches 0 of (1+2x)^x is 1