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

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
Plot the graph
Rapid solution [src] 
0
$$0$$
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
$$0$$ 
= 1.95647031552306e-17
     /1 - log(x)\
 lim |----------|
x->E-\    x     /
$$\lim_{x \to e^-}\left(\frac{1 - \log{\left(x \right)}}{x}\right)$$ 
0
$$0$$ 
= 1.95647031552307e-17
= 1.95647031552307e-17
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to e^-}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = 0$$
More at x→E from the left
$$\lim_{x \to e^+}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{1 - \log{\left(x \right)}}{x}\right) = 0$$
More at x→-oo
Numerical answer [src] 
1.95647031552306e-17
1.95647031552306e-17
The graph
Limit of the function (1-log(x))/x
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