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Limit of the function (1-log(x))/x

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     /1 - log(x)\
 lim |----------|
x->E+\    x     /

\lim_{x \to e^+}\left(\frac{1 - \log{\left(x \right)}}{x}\right)

Limit((1 - log(x))/x, x, E)

Lopital's rule

There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type

The graph

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Rapid solution [src]

0

Expand and simplify

One‐sided limits [src]

     /1 - log(x)\
 lim |----------|
x->E+\    x     /

\lim_{x \to e^+}\left(\frac{1 - \log{\left(x \right)}}{x}\right)

0

= 1.95647031552306e-17

     /1 - log(x)\
 lim |----------|
x->E-\    x     /

\lim_{x \to e^-}\left(\frac{1 - \log{\left(x \right)}}{x}\right)

0

= 1.95647031552307e-17

= 1.95647031552307e-17

Other limits x→0, -oo, +oo, 1

\lim_{x \to e^-}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = 0

\lim_{x \to e^+}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = 0

\lim_{x \to \infty}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = 0

\lim_{x \to 0^-}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = -\infty

\lim_{x \to 0^+}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = \infty

\lim_{x \to 1^-}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = 1

\lim_{x \to 1^+}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = 1

\lim_{x \to -\infty}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = 0

Numerical answer [src]

1.95647031552306e-17

1.95647031552306e-17

The graph