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

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

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limit as x approaches infinity of 1-e^x

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

- \infty

Solution steps

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

x \to \infty lim (1) = 1

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

= 1 - \infty

Apply Infinity Property:

c - \infty = - \infty

= - \infty

x \to - 1 lim (x^{2} + 4)

\int \frac{1}{5 + 2 x} d x

\int x - 9 cos (x) d x

y = \frac{5}{x}, y = \frac{5}{x ^{2}}, x = 6

x \to 0 lim (x^{x^{x}})

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