Mister Exam

Other calculators:

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

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

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     /     ________\
     |    /      2 |
 lim \x*\/  1 + x  /
x->oo
lim⁡x→∞(xx2+1)\lim_{x \to \infty}\left(x \sqrt{x^{2} + 1}\right) 
Limit(x*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
02468-8-6-4-2-1010-200200
Plot the graph
Rapid solution [src] 
oo
∞\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(xx2+1)=∞\lim_{x \to \infty}\left(x \sqrt{x^{2} + 1}\right) = \infty
lim⁡x→0−(xx2+1)=0\lim_{x \to 0^-}\left(x \sqrt{x^{2} + 1}\right) = 0
More at x→0 from the left
lim⁡x→0+(xx2+1)=0\lim_{x \to 0^+}\left(x \sqrt{x^{2} + 1}\right) = 0
More at x→0 from the right
lim⁡x→1−(xx2+1)=2\lim_{x \to 1^-}\left(x \sqrt{x^{2} + 1}\right) = \sqrt{2}
More at x→1 from the left
lim⁡x→1+(xx2+1)=2\lim_{x \to 1^+}\left(x \sqrt{x^{2} + 1}\right) = \sqrt{2}
More at x→1 from the right
lim⁡x→−∞(xx2+1)=−∞\lim_{x \to -\infty}\left(x \sqrt{x^{2} + 1}\right) = -\infty
More at x→-oo
The graph
Limit of the function x*sqrt(1+x^2)
    © Mister Exam – Calculator