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

The limit as x approaches infinity of ((5+2e^{-2x}))/(ln(x)) is 0

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

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

0

Solution steps

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

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

x \to \infty lim (ln (x)) = \infty

= \frac{5}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

17 - x^{2}

x \to 1 lim (\frac{1}{x})

4 - x^{2}, x = 0

- 2 x^{2} + 8 x, [- 1, 2]

4 x^{3} - 3 x^{4}

What is the limit as x approaches infinity of ((5+2e^{-2x}))/(ln(x)) ?
The limit as x approaches infinity of ((5+2e^{-2x}))/(ln(x)) is 0