What is the limit as x approaches infinity of 8-e^x ?

The limit as x approaches infinity of 8-e^x is -infinity

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limit as x approaches infinity of 8-e^x

x \to \infty lim (8 - e^{x})

- \infty

Solution steps

x \to \infty lim (8 - e^{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 (8) - x \to \infty lim (e^{x})

x \to \infty lim (8) = 8

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

= 8 - \infty

Apply Infinity Property:

c - \infty = - \infty

= - \infty

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What is the limit as x approaches infinity of 8-e^x ?
The limit as x approaches infinity of 8-e^x is -infinity