What is the limit as x approaches 0 of (e^{x^6}-1)/x ?

The limit as x approaches 0 of (e^{x^6}-1)/x is 0

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limit as x approaches 0 of (e^{x^6}-1)/x

x \to 0 lim (\frac{e ^{x^{6}} - 1}{x})

0

Solution steps

x \to 0 lim (\frac{e ^{x^{6}} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{6 e ^{x^{6}} x ^{5}}{1})

= x \to 0 lim (\frac{6 e ^{x^{6}} x ^{5}}{1})

Plug in the value

x = 0

= \frac{6 e ^{0^{6}} \cdot 0 ^{5}}{1}

Simplify

\frac{6 e ^{0^{6}} \cdot 0 ^{5}}{1} : 0

= 0

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What is the limit as x approaches 0 of (e^{x^6}-1)/x ?
The limit as x approaches 0 of (e^{x^6}-1)/x is 0