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

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

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

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

- 1

Solution steps

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

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 (1)

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

x \to - \infty lim (1) = 1

= 0 - 1

Simplify

= - 1

x \to \frac{π}{4} lim (\frac{sec ^{2} ( x ) - 2 tan ( x )}{1 + cos ( 4 x )})

y^{^{''}} - (\frac{6}{x}) y^{^{'}} - (\frac{9}{x ^{2}}) y = 0

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

x \to + 0 lim (\frac{1}{x})

x^{^{''}} + k x^{^{'}} + x = 0

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