What is the limit as x approaches infinity of (1+6x)^{3/x} ?

The limit as x approaches infinity of (1+6x)^{3/x} is 1

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limit as x approaches infinity of (1+6x)^{3/x}

x \to \infty lim ((1 + 6 x)^{\frac{3}{x}})

1

Solution steps

x \to \infty lim ((1 + 6 x)^{\frac{3}{x}})

Apply exponent rules

= x \to \infty lim (e^{\frac{3}{x} l n (1 + 6 x)})

Apply the Limit Chain Rule:

1

= 1

What is the limit as x approaches infinity of (1+6x)^{3/x} ?
The limit as x approaches infinity of (1+6x)^{3/x} is 1