What is the limit as x approaches 0 of (1+6x)^{1/x} ?

The limit as x approaches 0 of (1+6x)^{1/x} is e^6

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limit as x approaches 0 of (1+6x)^{1/x}

x \to 0 lim ((1 + 6 x)^{\frac{1}{x}})

e^{6}

Decimal Notation

403.42879 \dots

Solution steps

x \to 0 lim ((1 + 6 x)^{\frac{1}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{1}{x} l n (1 + 6 x)})

Apply the Limit Chain Rule:

e^{6}

= e^{6}

x \to 0 lim (\frac{2 x ^{2} + x}{5 x})

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

x \to 0 + lim (5 x ln (x))

x \to 0 lim (\frac{sin ( ω ) x}{x})

x \to 0 lim (- 1 + x)

What is the limit as x approaches 0 of (1+6x)^{1/x} ?
The limit as x approaches 0 of (1+6x)^{1/x} is e^6