What is the limit as x approaches-infinity of (-5e^x+5)/(3+8e^x) ?

The limit as x approaches-infinity of (-5e^x+5)/(3+8e^x) is 5/3

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limit as x approaches-infinity of (-5e^x+5)/(3+8e^x)

x \to - \infty lim (\frac{- 5 e ^{x} + 5}{3 + 8 e ^{x}})

\frac{5}{3}

Decimal Notation

1.66666 \dots

Solution steps

x \to - \infty lim (\frac{- 5 e ^{x} + 5}{3 + 8 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} ( - 5 e ^{x} + 5 )}{lim _{x \to - \infty} ( 3 + 8 e ^{x} )}

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

x \to - \infty lim (3 + 8 e^{x}) = 3

= \frac{5}{3}

x \to 0 lim (x^{\frac{1}{f ( x )}})

x \to 0 lim (x cos (\frac{1}{x}) + 2)

n \to \infty lim (sin (2 πn))

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

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

What is the limit as x approaches-infinity of (-5e^x+5)/(3+8e^x) ?
The limit as x approaches-infinity of (-5e^x+5)/(3+8e^x) is 5/3