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x-2/x
Limit of the function/ x-2/x

Limit of the function x-2/x

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     /    2\
 lim |x - -|
x->4+\    x/
lim⁡x→4+(x−2x)\lim_{x \to 4^+}\left(x - \frac{2}{x}\right) 
Limit(x - 2/x, x, 4)
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
80246-8-6-4-2-5050
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→4−(x−2x)=72\lim_{x \to 4^-}\left(x - \frac{2}{x}\right) = \frac{7}{2}
More at x→4 from the left
lim⁡x→4+(x−2x)=72\lim_{x \to 4^+}\left(x - \frac{2}{x}\right) = \frac{7}{2}
lim⁡x→∞(x−2x)=∞\lim_{x \to \infty}\left(x - \frac{2}{x}\right) = \infty
More at x→oo
lim⁡x→0−(x−2x)=∞\lim_{x \to 0^-}\left(x - \frac{2}{x}\right) = \infty
More at x→0 from the left
lim⁡x→0+(x−2x)=−∞\lim_{x \to 0^+}\left(x - \frac{2}{x}\right) = -\infty
More at x→0 from the right
lim⁡x→1−(x−2x)=−1\lim_{x \to 1^-}\left(x - \frac{2}{x}\right) = -1
More at x→1 from the left
lim⁡x→1+(x−2x)=−1\lim_{x \to 1^+}\left(x - \frac{2}{x}\right) = -1
More at x→1 from the right
lim⁡x→−∞(x−2x)=−∞\lim_{x \to -\infty}\left(x - \frac{2}{x}\right) = -\infty
More at x→-oo
Rapid solution [src] 
7/2
72\frac{7}{2}
Expand and simplify
One‐sided limits [src] 
     /    2\
 lim |x - -|
x->4+\    x/
lim⁡x→4+(x−2x)\lim_{x \to 4^+}\left(x - \frac{2}{x}\right) 
7/2
72\frac{7}{2} 
= 3.5
     /    2\
 lim |x - -|
x->4-\    x/
lim⁡x→4−(x−2x)\lim_{x \to 4^-}\left(x - \frac{2}{x}\right) 
7/2
72\frac{7}{2} 
= 3.5
= 3.5
Numerical answer [src] 
3.5
3.5
The graph
Limit of the function x-2/x
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