What is the limit as x approaches infinity of 4e^{-x}+6x-3 ?

The limit as x approaches infinity of 4e^{-x}+6x-3 is infinity

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limit as x approaches infinity of 4e^{-x}+6x-3

x \to \infty lim (4 e^{- x} + 6 x - 3)

\infty

Solution steps

x \to \infty lim (4 e^{- x} + 6 x - 3)

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 (4 e^{- x}) + x \to \infty lim (6 x) - x \to \infty lim (3)

x \to \infty lim (4 e^{- x}) = 0

x \to \infty lim (6 x) = \infty

x \to \infty lim (3) = 3

= 0 + \infty - 3

Simplify

0 + \infty - 3 : \infty

= \infty

What is the limit as x approaches infinity of 4e^{-x}+6x-3 ?
The limit as x approaches infinity of 4e^{-x}+6x-3 is infinity