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

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

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limit as x approaches infinity of e^x-e

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

\infty

Solution steps

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

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

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

x \to \infty lim (e) = e

= \infty - e

Apply Infinity Property:

\infty - c = \infty

= \infty

x \to \infty lim (- 15)

x \to - 0.1 lim (\frac{( e ^{x} - 1 )}{x})

x \to 0 lim (x^{3} - x^{2} + x - 1)

x \to - 3 lim (x^{4} + 9 x^{2} - 11 x)

x \to 3 lim (\frac{x ^{3} - 3 x ^{2}}{5 x - 15})

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