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x-sqrt(x)
Limit of the function/ x-sqrt(x)

Limit of the function x-sqrt(x)

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The solution

You have entered [src] 
     /      ___\
 lim \x - \/ x /
x->1+
lim⁡x→1+(−x+x)\lim_{x \to 1^+}\left(- \sqrt{x} + x\right) 
Limit(x - sqrt(x), x, 1)
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
-2.0-1.5-1.0-0.52.00.00.51.01.51.0-1.0
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→1−(−x+x)=0\lim_{x \to 1^-}\left(- \sqrt{x} + x\right) = 0
More at x→1 from the left
lim⁡x→1+(−x+x)=0\lim_{x \to 1^+}\left(- \sqrt{x} + x\right) = 0
lim⁡x→∞(−x+x)=∞\lim_{x \to \infty}\left(- \sqrt{x} + x\right) = \infty
More at x→oo
lim⁡x→0−(−x+x)=0\lim_{x \to 0^-}\left(- \sqrt{x} + x\right) = 0
More at x→0 from the left
lim⁡x→0+(−x+x)=0\lim_{x \to 0^+}\left(- \sqrt{x} + x\right) = 0
More at x→0 from the right
lim⁡x→−∞(−x+x)=−∞\lim_{x \to -\infty}\left(- \sqrt{x} + x\right) = -\infty
More at x→-oo
One‐sided limits [src] 
     /      ___\
 lim \x - \/ x /
x->1+
lim⁡x→1+(−x+x)\lim_{x \to 1^+}\left(- \sqrt{x} + x\right) 
0
00 
= -1.06414145882481e-30
     /      ___\
 lim \x - \/ x /
x->1-
lim⁡x→1−(−x+x)\lim_{x \to 1^-}\left(- \sqrt{x} + x\right) 
0
00 
= -7.17592337510183e-33
= -7.17592337510183e-33
Numerical answer [src] 
-1.06414145882481e-30
-1.06414145882481e-30
The graph
Limit of the function x-sqrt(x)
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