What is the limit as x approaches infinity of arccos(1-3^{-x}) ?

The limit as x approaches infinity of arccos(1-3^{-x}) is 0

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limit as x approaches infinity of arccos(1-3^{-x})

x \to \infty lim (arccos (1 - 3^{- x}))

0

Solution steps

x \to \infty lim (arccos (1 - 3^{- x}))

Apply the Limit Chain Rule:

0

= 0

x \to π lim (cos (\frac{x}{2}))

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

x \to 5 lim (\frac{3 x - 2}{x - 5})

x \to \frac{1}{2} lim (\frac{1}{1 - 2 x})

x \to - 2 lim (- x^{4} + 8 x^{2})

What is the limit as x approaches infinity of arccos(1-3^{-x}) ?
The limit as x approaches infinity of arccos(1-3^{-x}) is 0