What is the limit as x approaches-infinity of e^x-3x ?

The limit as x approaches-infinity of e^x-3x is infinity

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limit as x approaches-infinity of e^x-3x

x \to - \infty lim (e^{x} - 3 x)

\infty

Solution steps

x \to - \infty lim (e^{x} - 3 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 (e^{x}) - x \to - \infty lim (3 x)

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

x \to - \infty lim (3 x) = - \infty

= 0 - (- \infty)

Simplify

0 - (- \infty) : \infty

= \infty

What is the limit as x approaches-infinity of e^x-3x ?
The limit as x approaches-infinity of e^x-3x is infinity