What is the limit as x approaches 1-of (1+2x)^{1/x} ?

The limit as x approaches 1-of (1+2x)^{1/x} is 3

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limit as x approaches 1-of (1+2x)^{1/x}

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

3

Solution steps

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

Plug in the value

x = 1

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

Simplify

= 3

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

x \to - 2 lim (\frac{1 - 2 π}{x + 2})

x \to 1 + lim (3 x + 1)

x \to \frac{2}{3} lim (3 - 4 x + 5 x^{2})

x \to 1 lim (4 ln (x))

What is the limit as x approaches 1-of (1+2x)^{1/x} ?
The limit as x approaches 1-of (1+2x)^{1/x} is 3