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

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

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

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

e^{7}

Decimal Notation

1096.63315 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{7}

= e^{7}

\int \frac{2 x ^{5} - 4 x + 8 x}{x} d x

ln (1 + e^{x})

\frac{d}{d x} (arcsin (2 x^{4}))

\int \frac{x ^{2} + 4 x + 7}{x ^{2} - 6 x + 5} d x

\int_{0}^{t} e^{- x} d x

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