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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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You have entered [src] 
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 lim \/  5 + x  
x->oo
lim⁡x→∞x2+5\lim_{x \to \infty} \sqrt{x^{2} + 5} 
Limit(sqrt(5 + x^2), x, oo, dir='-')
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
02468-8-6-4-2-1010020
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Rapid solution [src] 
oo
∞\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞x2+5=∞\lim_{x \to \infty} \sqrt{x^{2} + 5} = \infty
lim⁡x→0−x2+5=5\lim_{x \to 0^-} \sqrt{x^{2} + 5} = \sqrt{5}
More at x→0 from the left
lim⁡x→0+x2+5=5\lim_{x \to 0^+} \sqrt{x^{2} + 5} = \sqrt{5}
More at x→0 from the right
lim⁡x→1−x2+5=6\lim_{x \to 1^-} \sqrt{x^{2} + 5} = \sqrt{6}
More at x→1 from the left
lim⁡x→1+x2+5=6\lim_{x \to 1^+} \sqrt{x^{2} + 5} = \sqrt{6}
More at x→1 from the right
lim⁡x→−∞x2+5=∞\lim_{x \to -\infty} \sqrt{x^{2} + 5} = \infty
More at x→-oo
The graph
Limit of the function sqrt(5+x^2)
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