What is the limit as x approaches-infinity of e^x-2 ?

The limit as x approaches-infinity of e^x-2 is -2

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limit as x approaches-infinity of e^x-2

x \to - \infty lim (e^{x} - 2)

- 2

Solution steps

x \to - \infty lim (e^{x} - 2)

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 (2)

x \to - \infty lim (e^{x}) = 0

x \to - \infty lim (2) = 2

= 0 - 2

Simplify

= - 2

x \to - 8 - lim (\frac{3 - 4 x}{x + 8})

x \to - 2 lim (x^{3} - 3 x^{2} + 4 x - 1)

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

x \to - 1 lim (1 - 4 x)

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

What is the limit as x approaches-infinity of e^x-2 ?
The limit as x approaches-infinity of e^x-2 is -2