What is the limit as x approaches infinity of (ln(5))/((1+ln(x))) ?

The limit as x approaches infinity of (ln(5))/((1+ln(x))) is 0

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limit as x approaches infinity of (ln(5))/((1+ln(x)))

x \to \infty lim (\frac{ln ( 5 )}{( 1 + ln ( x ) )})

0

Solution steps

x \to \infty lim (\frac{ln ( 5 )}{1 + ln ( x )})

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

= ln (5) \cdot x \to \infty lim (\frac{1}{1 + 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

= ln (5) \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( 1 + ln ( x ) )}

x \to \infty lim (1) = 1

x \to \infty lim (1 + ln (x)) = \infty

= ln (5) \frac{1}{\infty}

Simplify

ln (5) \frac{1}{\infty} : 0

= 0

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\int_{2}^{\infty} \frac{8 cos ( \frac{π}{x} )}{x ^{2}} d x

What is the limit as x approaches infinity of (ln(5))/((1+ln(x))) ?
The limit as x approaches infinity of (ln(5))/((1+ln(x))) is 0