What is the limit as x approaches infinity of (4^x+3^x)^{1/x} ?

The limit as x approaches infinity of (4^x+3^x)^{1/x} is 4

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limit as x approaches infinity of (4^x+3^x)^{1/x}

x \to \infty lim ((4^{x} + 3^{x})^{\frac{1}{x}})

4

Solution steps

x \to \infty lim ((4^{x} + 3^{x})^{\frac{1}{x}})

Apply exponent rules

= x \to \infty lim (e^{\frac{1}{x} l n (4^{x} + 3^{x})})

Apply the Limit Chain Rule:

4

= 4

\int_{1}^{5} (5 x - \frac{5}{x}) d x

x \to 3 lim (\frac{x - 4}{x - 3})

\int 5 tan (x) sec^{3} (x) d x

x \to 4 lim (e^{4 - x})

\frac{\partial}{\partial x} (x y^{3} + x^{2})

What is the limit as x approaches infinity of (4^x+3^x)^{1/x} ?
The limit as x approaches infinity of (4^x+3^x)^{1/x} is 4