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

The limit as x approaches 0 of (x+e^{x/6})^{6/x} is e^7

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

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

e^{7}

Decimal Notation

1096.63315 \dots

Solution steps

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

Apply exponent rules

= x \to 0 lim (e^{\frac{6}{x} l n (x + e^{\frac{x}{6}})})

Apply the Limit Chain Rule:

e^{7}

= e^{7}

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

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What is the limit as x approaches 0 of (x+e^{x/6})^{6/x} ?
The limit as x approaches 0 of (x+e^{x/6})^{6/x} is e^7