What is the limit as x approaches infinity of (3^x+2^x)^{1/x} ?

The limit as x approaches infinity of (3^x+2^x)^{1/x} is 3

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limit as x approaches infinity of (3^x+2^x)^{1/x}

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

3

Solution steps

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

Apply exponent rules

= x \to \infty lim (e^{\frac{1}{x} l n (3^{x} + 2^{x})})

Apply the Limit Chain Rule:

3

= 3

What is the limit as x approaches infinity of (3^x+2^x)^{1/x} ?
The limit as x approaches infinity of (3^x+2^x)^{1/x} is 3