What is the limit as x approaches 0 of (1+7x)^{2/x} ?

The limit as x approaches 0 of (1+7x)^{2/x} is e^{14}

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limit as x approaches 0 of (1+7x)^{2/x}

x \to 0 lim ((1 + 7 x)^{\frac{2}{x}})

e^{14}

Decimal Notation

1202604.28416 \dots

Solution steps

x \to 0 lim ((1 + 7 x)^{\frac{2}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{2}{x} l n (1 + 7 x)})

Apply the Limit Chain Rule:

e^{14}

= e^{14}

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What is the limit as x approaches 0 of (1+7x)^{2/x} ?
The limit as x approaches 0 of (1+7x)^{2/x} is e^{14}