What is the limit as x approaches 0+of (1+x^3)^{2/x} ?

The limit as x approaches 0+of (1+x^3)^{2/x} is 1

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limit as x approaches 0+of (1+x^3)^{2/x}

x \to 0 + lim ((1 + x^{3})^{\frac{2}{x}})

1

Solution steps

x \to 0 + lim ((1 + x^{3})^{\frac{2}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{2}{x} l n (1 + x^{3})})

Apply the Limit Chain Rule:

1

= 1

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

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

x \to \frac{π}{2} lim (sin (\frac{π}{2}))

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

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

What is the limit as x approaches 0+of (1+x^3)^{2/x} ?
The limit as x approaches 0+of (1+x^3)^{2/x} is 1