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

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

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     /1         \
 lim |- + log(x)|
x->0+\x         /
$$\lim_{x \to 0^+}\left(\log{\left(x \right)} + \frac{1}{x}\right)$$ 
Limit(1/x + log(x), x, 0)
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\log{\left(x \right)} + \frac{1}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\log{\left(x \right)} + \frac{1}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\log{\left(x \right)} + \frac{1}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\log{\left(x \right)} + \frac{1}{x}\right) = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\log{\left(x \right)} + \frac{1}{x}\right) = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\log{\left(x \right)} + \frac{1}{x}\right) = \infty$$
More at x→-oo
Rapid solution [src] 
oo
$$\infty$$
Expand and simplify
One‐sided limits [src] 
     /1         \
 lim |- + log(x)|
x->0+\x         /
$$\lim_{x \to 0^+}\left(\log{\left(x \right)} + \frac{1}{x}\right)$$ 
oo
$$\infty$$ 
= 145.982720163185
     /1         \
 lim |- + log(x)|
x->0-\x         /
$$\lim_{x \to 0^-}\left(\log{\left(x \right)} + \frac{1}{x}\right)$$ 
-oo
$$-\infty$$ 
= (-156.017279836815 + 3.14159265358979j)
= (-156.017279836815 + 3.14159265358979j)
Numerical answer [src] 
145.982720163185
145.982720163185
The graph
Limit of the function 1/x+log(x)
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