What is the limit as x approaches-infinity of e^{3x}(2-x) ?

The limit as x approaches-infinity of e^{3x}(2-x) is 0

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limit as x approaches-infinity of e^{3x}(2-x)

x \to - \infty lim (e^{3 x} (2 - x))

0

Solution steps

x \to - \infty lim (e^{3 x} (2 - x))

Factor out

x

from

2 - x : x (\frac{- 2}{- x} - 1)

= x \to - \infty lim (e^{3 x} x (\frac{- 2}{- x} - 1))

Simplify

e^{3 x} x (\frac{- 2}{- x} - 1) : 2 e^{3 x} - e^{3 x} x

= x \to - \infty lim (2 e^{3 x} - e^{3 x} 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 (2 e^{3 x}) - x \to - \infty lim (e^{3 x} x)

x \to - \infty lim (2 e^{3 x}) = 0

x \to - \infty lim (e^{3 x} x) = 0

= 0 - 0

Simplify

= 0

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What is the limit as x approaches-infinity of e^{3x}(2-x) ?
The limit as x approaches-infinity of e^{3x}(2-x) is 0