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

The limit as x approaches infinity of (5e^{-3x}+2)/(e^{-5x)+4} is 1/2

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

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

\frac{1}{2}

Decimal

0.5

Solution steps

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

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

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

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

= \frac{2}{4}

Cancel the common factor:

2

= \frac{1}{2}

What is the limit as x approaches infinity of (5e^{-3x}+2)/(e^{-5x)+4} ?
The limit as x approaches infinity of (5e^{-3x}+2)/(e^{-5x)+4} is 1/2