Mister Exam

Other calculators:

sqrt(10-x^2)
Limit of the function/ sqrt(10-x^2)

Limit of the function sqrt(10-x^2)

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
        _________
       /       2 
 lim \/  10 - x  
x->3+
lim⁡x→3+10−x2\lim_{x \to 3^+} \sqrt{10 - x^{2}} 
Limit(sqrt(10 - x^2), x, 3)
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
6012345-6-5-4-3-2-10.05.0
Plot the graph
Rapid solution [src] 
1
11
Expand and simplify
One‐sided limits [src] 
        _________
       /       2 
 lim \/  10 - x  
x->3+
lim⁡x→3+10−x2\lim_{x \to 3^+} \sqrt{10 - x^{2}} 
1
11 
= 1.0
        _________
       /       2 
 lim \/  10 - x  
x->3-
lim⁡x→3−10−x2\lim_{x \to 3^-} \sqrt{10 - x^{2}} 
1
11 
= 1.0
= 1.0
Other limits x→0, -oo, +oo, 1
lim⁡x→3−10−x2=1\lim_{x \to 3^-} \sqrt{10 - x^{2}} = 1
More at x→3 from the left
lim⁡x→3+10−x2=1\lim_{x \to 3^+} \sqrt{10 - x^{2}} = 1
lim⁡x→∞10−x2=∞i\lim_{x \to \infty} \sqrt{10 - x^{2}} = \infty i
More at x→oo
lim⁡x→0−10−x2=10\lim_{x \to 0^-} \sqrt{10 - x^{2}} = \sqrt{10}
More at x→0 from the left
lim⁡x→0+10−x2=10\lim_{x \to 0^+} \sqrt{10 - x^{2}} = \sqrt{10}
More at x→0 from the right
lim⁡x→1−10−x2=3\lim_{x \to 1^-} \sqrt{10 - x^{2}} = 3
More at x→1 from the left
lim⁡x→1+10−x2=3\lim_{x \to 1^+} \sqrt{10 - x^{2}} = 3
More at x→1 from the right
lim⁡x→−∞10−x2=∞i\lim_{x \to -\infty} \sqrt{10 - x^{2}} = \infty i
More at x→-oo
Numerical answer [src] 
1.0
1.0
The graph
Limit of the function sqrt(10-x^2)
    © Mister Exam – Calculator