What is the limit as x approaches infinity of (4^x+8^x)^{1/(2*x)} ?

The limit as x approaches infinity of (4^x+8^x)^{1/(2*x)} is 2sqrt(2)

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limit as x approaches infinity of (4^x+8^x)^{1/(2*x)}

x \to \infty lim ((4^{x} + 8^{x})^{\frac{1}{2 \cdot x}})

22

Decimal Notation

2.82842 \dots

Solution steps

x \to \infty lim ((4^{x} + 8^{x})^{\frac{1}{2 x}})

Apply exponent rules

= x \to \infty lim (e^{\frac{1}{2 x} l n (4^{x} + 8^{x})})

Apply the Limit Chain Rule:

22

= 22

\frac{d}{d x} (- x cos (x) + x)

\frac{\partial}{\partial y} (x^{4} + y^{4} + 3 x^{2} y^{3})

\frac{\partial}{\partial x} (x e^{- x^{2}})

\frac{1}{s + 1 ( - 2 s + 10 )}

n = 1 \sum \infty \frac{( - 5 ) ^{n}}{3 ^{2 n + 1}}

What is the limit as x approaches infinity of (4^x+8^x)^{1/(2*x)} ?
The limit as x approaches infinity of (4^x+8^x)^{1/(2*x)} is 2sqrt(2)