What is the limit as x approaches infinity of 1/(x*log_{e)(x)} ?

The limit as x approaches infinity of 1/(x*log_{e)(x)} is 0

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limit as x approaches infinity of 1/(x*log_{e)(x)}

x \to \infty lim (\frac{1}{x \cdot lo g _{e} ( x )})

0

Solution steps

x \to \infty lim (\frac{1}{x lo g _{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} ( 1 )}{lim _{x \to \infty} ( x lo g _{e} ( x ) )}

x \to \infty lim (1) = 1

x \to \infty lim (x lo g_{e} (x)) = \infty

= \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

x \to 2 - lim (\frac{x - 2}{x - 2})

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

\int \frac{3}{( 5 v - 1 ) ^{4}} d v

\frac{d}{d x} (cos (x) - x)

(x - 5)^{2} + (y - 3)^{2} = 18, (8, 6)

What is the limit as x approaches infinity of 1/(x*log_{e)(x)} ?
The limit as x approaches infinity of 1/(x*log_{e)(x)} is 0