What is the limit as x approaches-infinity of 9e^{2x}-7e^{-14x}-e^x ?

The limit as x approaches-infinity of 9e^{2x}-7e^{-14x}-e^x is -infinity

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limit as x approaches-infinity of 9e^{2x}-7e^{-14x}-e^x

x \to - \infty lim (9 e^{2 x} - 7 e^{- 14 x} - e^{x})

- \infty

Solution steps

x \to - \infty lim (9 e^{2 x} - 7 e^{- 14 x} - 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 (9 e^{2 x}) - x \to - \infty lim (7 e^{- 14 x}) - x \to - \infty lim (e^{x})

x \to - \infty lim (9 e^{2 x}) = 0

x \to - \infty lim (7 e^{- 14 x}) = \infty

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

= 0 - \infty - 0

Simplify

0 - \infty - 0 : - \infty

= - \infty

What is the limit as x approaches-infinity of 9e^{2x}-7e^{-14x}-e^x ?
The limit as x approaches-infinity of 9e^{2x}-7e^{-14x}-e^x is -infinity