What is the limit as x approaches infinity of 1-1^x ?

The limit as x approaches infinity of 1-1^x is 0

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limit as x approaches infinity of 1-1^x

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

0

Solution steps

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

x \to \infty lim (1) = 1

x \to \infty lim (1^{x}) = 1

= 1 - 1

Simplify

= 0

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What is the limit as x approaches infinity of 1-1^x ?
The limit as x approaches infinity of 1-1^x is 0