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

The limit as x approaches 3 of (1+2x)^{1/3}x is 3*7^{1/3}

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

x \to 3 lim ((1 + 2 x)^{\frac{1}{3}} x)

3 \cdot 7^{\frac{1}{3}}

Decimal

5.73879 \dots

Solution steps

x \to 3 lim ((1 + 2 x)^{\frac{1}{3}} x)

Plug in the value

x = 3

= (1 + 2 \cdot 3)^{\frac{1}{3}} \cdot 3

Simplify

= 3 \cdot 7^{\frac{1}{3}}

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

x \to 3 lim (\frac{( e ^{x} - 1 ) ^{2}}{x})

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

x \to 3 lim (4 x - 2 x - 5)

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

What is the limit as x approaches 3 of (1+2x)^{1/3}x ?
The limit as x approaches 3 of (1+2x)^{1/3}x is 3*7^{1/3}