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

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

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limit as x approaches 0 of (e^{x^3}-1)/x

x \to 0 lim (\frac{e ^{x^{3}} - 1}{x})

0

Solution steps

x \to 0 lim (\frac{e ^{x^{3}} - 1}{x})

Apply L'Hopital's Rule

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

Plug in the value

x = 0

= \frac{3 e ^{0^{3}} \cdot 0 ^{2}}{1}

Simplify

\frac{3 e ^{0^{3}} \cdot 0 ^{2}}{1} : 0

= 0

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