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

The limit as x approaches 0 of (e^x+x)^{6/x} is e^{12}

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

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

e^{12}

Decimal

162754.79141 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{12}

= e^{12}

x \to 2 - lim (\frac{1}{( x - 2 ) ^{3}})

x \to \frac{3 π}{2} lim (x sec (x))

x \to 3 + lim (\frac{x}{2} + 1)

x \to 7 + lim (\frac{6}{x - 7})

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

What is the limit as x approaches 0 of (e^x+x)^{6/x} ?
The limit as x approaches 0 of (e^x+x)^{6/x} is e^{12}