What is the limit as x approaches infinity of \sqrt[x]{6^x+7^x+8^x} ?

The limit as x approaches infinity of \sqrt[x]{6^x+7^x+8^x} is 8

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limit as x approaches infinity of \sqrt[x]{6^x+7^x+8^x}

x \to \infty lim (x 6^{x} + 7^{x} + 8^{x})

8

Solution steps

x \to \infty lim (x 6^{x} + 7^{x} + 8^{x})

Apply exponent rules

= x \to \infty lim (e^{\frac{1}{x} l n (6^{x} + 7^{x} + 8^{x})})

Apply the Limit Chain Rule:

8

= 8

x \to 1 lim (x^{2} - 17)

t \to 0 lim (\frac{e ^{5 t} - 1}{sin ( t )})

x \to \infty lim (12 x^{3})

x \to 0 lim ((1 + \frac{4}{x ^{5}})^{x})

x \to 0 lim (x^{2} + 2 x - 1)

What is the limit as x approaches infinity of \sqrt[x]{6^x+7^x+8^x} ?
The limit as x approaches infinity of \sqrt[x]{6^x+7^x+8^x} is 8