What is the limit as x approaches infinity of (3.4)/(0.1+33.9e^{-0.5678x)} ?

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limit as x approaches infinity of (3.4)/(0.1+33.9e^{-0.5678x)}

x \to \infty lim (\frac{3.4}{0.1 + 33.9 e ^{- 0.5678 x}})

34

Solution steps

x \to \infty lim (\frac{3.4}{0.1 + 33.9 e ^{- 0.5678 x}})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 3.4 \cdot x \to \infty lim (\frac{1}{0.1 + 33.9 e ^{- 0.5678 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

= 3.4 \cdot \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( 0.1 + 33.9 e ^{- 0.5678 x} )}

x \to \infty lim (1) = 1

x \to \infty lim (0.1 + 33.9 e^{- 0.5678 x}) = 0.1

= 3.4 \cdot \frac{1}{0.1}

Simplify

3.4 \cdot \frac{1}{0.1} : 34

= 34

t^{3} 1 (t)

\frac{d}{d x} (\frac{ln ( x )}{5 ln ( x ) + 4})

\int_{1}^{4} t ln (t) d t

y = x + 3 y = x + 1 y = - x + 1

\frac{d}{d x} (\frac{3 x + 2}{x - 1})

What is the limit as x approaches infinity of (3.4)/(0.1+33.9e^{-0.5678x)} ?
The limit as x approaches infinity of (3.4)/(0.1+33.9e^{-0.5678x)} is 34