What is the limit as x approaches-infinity of (2-3e^{-x})/(5e^{-x)-4} ?

The limit as x approaches-infinity of (2-3e^{-x})/(5e^{-x)-4} is -3/5

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limit as x approaches-infinity of (2-3e^{-x})/(5e^{-x)-4}

x \to - \infty lim (\frac{2 - 3 e ^{- x}}{5 e ^{- x} - 4})

- \frac{3}{5}

Decimal

- 0.6

Solution steps

x \to - \infty lim (\frac{2 - 3 e ^{- x}}{5 e ^{- x} - 4})

Divide by

e^{- x} : \frac{2 e ^{x} - 3}{5 - 4 e ^{x}}

= x \to - \infty lim (\frac{2 e ^{x} - 3}{5 - 4 e ^{x}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to - \infty} ( 2 e ^{x} - 3 )}{lim _{x \to - \infty} ( 5 - 4 e ^{x} )}

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

x \to - \infty lim (5 - 4 e^{x}) = 5

= \frac{- 3}{5}

Simplify

= - \frac{3}{5}

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

x \to 1 lim (\frac{π}{x - 1})

x \to 0 lim (x^{2} sin (\frac{2}{x}))

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

t \to 0 lim (\frac{sin ( t ^{2} )}{t})

What is the limit as x approaches-infinity of (2-3e^{-x})/(5e^{-x)-4} ?
The limit as x approaches-infinity of (2-3e^{-x})/(5e^{-x)-4} is -3/5