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x-6/x
Limit of the function/ x-6/x

Limit of the function x-6/x

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     /    6\
 lim |x - -|
x->6+\    x/
$$\lim_{x \to 6^+}\left(x - \frac{6}{x}\right)$$ 
Limit(x - 6/x, x, 6)
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] 
5
$$5$$
Expand and simplify
One‐sided limits [src] 
     /    6\
 lim |x - -|
x->6+\    x/
$$\lim_{x \to 6^+}\left(x - \frac{6}{x}\right)$$ 
5
$$5$$ 
= 5.0
     /    6\
 lim |x - -|
x->6-\    x/
$$\lim_{x \to 6^-}\left(x - \frac{6}{x}\right)$$ 
5
$$5$$ 
= 5.0
= 5.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 6^-}\left(x - \frac{6}{x}\right) = 5$$
More at x→6 from the left
$$\lim_{x \to 6^+}\left(x - \frac{6}{x}\right) = 5$$
$$\lim_{x \to \infty}\left(x - \frac{6}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(x - \frac{6}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x - \frac{6}{x}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x - \frac{6}{x}\right) = -5$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x - \frac{6}{x}\right) = -5$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x - \frac{6}{x}\right) = -\infty$$
More at x→-oo
Numerical answer [src] 
5.0
5.0
The graph
Limit of the function x-6/x
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