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}

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}

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\frac{d}{d x} (\frac{( x ^{2} + 1 ) ^{2}}{( x ^{4} + 1 ) ^{4}})

x \to 2 lim (\frac{2 x - 8}{x - 1})

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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