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sqrt(5-x^2)
Limit of the function/ sqrt(5-x^2)

Limit of the function sqrt(5-x^2)

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        ________
       /      2 
 lim \/  5 - x  
x->1+
lim⁡x→1+5−x2\lim_{x \to 1^+} \sqrt{5 - x^{2}} 
Limit(sqrt(5 - x^2), 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
-2.0-1.5-1.0-0.52.00.00.51.01.503
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→1−5−x2=2\lim_{x \to 1^-} \sqrt{5 - x^{2}} = 2
More at x→1 from the left
lim⁡x→1+5−x2=2\lim_{x \to 1^+} \sqrt{5 - x^{2}} = 2
lim⁡x→∞5−x2=∞i\lim_{x \to \infty} \sqrt{5 - x^{2}} = \infty i
More at x→oo
lim⁡x→0−5−x2=5\lim_{x \to 0^-} \sqrt{5 - x^{2}} = \sqrt{5}
More at x→0 from the left
lim⁡x→0+5−x2=5\lim_{x \to 0^+} \sqrt{5 - x^{2}} = \sqrt{5}
More at x→0 from the right
lim⁡x→−∞5−x2=∞i\lim_{x \to -\infty} \sqrt{5 - x^{2}} = \infty i
More at x→-oo
Rapid solution [src] 
2
22
Expand and simplify
One‐sided limits [src] 
        ________
       /      2 
 lim \/  5 - x  
x->1+
lim⁡x→1+5−x2\lim_{x \to 1^+} \sqrt{5 - x^{2}} 
2
22 
= 2.0
        ________
       /      2 
 lim \/  5 - x  
x->1-
lim⁡x→1−5−x2\lim_{x \to 1^-} \sqrt{5 - x^{2}} 
2
22 
= 2.0
= 2.0
Numerical answer [src] 
2.0
2.0
The graph
Limit of the function sqrt(5-x^2)
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