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

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

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

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

1

Solution steps

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

Plug in the value

x = 0

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

Simplify

= 1

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

x \to - 1 lim (\frac{x}{x ^{3} + 1})

x \to 25 lim (25 - x)

x \to 0 lim ((1 - x) \frac{1}{2 x})

x \to 4 - lim (\frac{2 x - 14}{x - 4})

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