What is the limit of $f (x) = \frac{1 + 4 e^{- x}}{3 - 2 e^{- x}}$ $f(x) = (1 + 4e^-x )/( 3 - 2e^-x)$ as x goes to infinity?

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Answer 1 · 2015-09-26T18:04:46

$lim_(xrarroo)(1 + 4e^-x )/( 3 - 2e^-x) = 1/3$

As $xrarroo$ , we have $e^-x rarr 0$ , so $1+4e^-x rarr 1$ while $3-2e^-x rarr 3$ .

Interestingly, as $xrarr-oo$ we get a different limit. We have
$lim_(xrarr-oo)(1 + 4e^-x )/( 3 - 2e^-x) = 4/-2 =-2$

What is the limit of f(x) = (1 + 4e^-x )/( 3 - 2e^-x)f(x)=1+4e−x3−2e−xf(x) = (1 + 4e^-x )/( 3 - 2e^-x) as x goes to infinity?