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1/sqrt(1+x^2)
Limit of the function/ 1/sqrt(1+x^2)

Limit of the function 1/sqrt(1+x^2)

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          1     
 lim -----------
x->oo   ________
       /      2 
     \/  1 + x
lim⁡x→∞1x2+1\lim_{x \to \infty} \frac{1}{\sqrt{x^{2} + 1}} 
Limit(1/(sqrt(1 + 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
02468-8-6-4-2-10100.02.0
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→∞1x2+1=0\lim_{x \to \infty} \frac{1}{\sqrt{x^{2} + 1}} = 0
lim⁡x→0−1x2+1=1\lim_{x \to 0^-} \frac{1}{\sqrt{x^{2} + 1}} = 1
More at x→0 from the left
lim⁡x→0+1x2+1=1\lim_{x \to 0^+} \frac{1}{\sqrt{x^{2} + 1}} = 1
More at x→0 from the right
lim⁡x→1−1x2+1=22\lim_{x \to 1^-} \frac{1}{\sqrt{x^{2} + 1}} = \frac{\sqrt{2}}{2}
More at x→1 from the left
lim⁡x→1+1x2+1=22\lim_{x \to 1^+} \frac{1}{\sqrt{x^{2} + 1}} = \frac{\sqrt{2}}{2}
More at x→1 from the right
lim⁡x→−∞1x2+1=0\lim_{x \to -\infty} \frac{1}{\sqrt{x^{2} + 1}} = 0
More at x→-oo
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Limit of the function 1/sqrt(1+x^2)
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