Mister Exam

Other calculators:

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

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

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     /    x    \
 lim |---------|
x->0+|  _______|
     \\/ 1 + x /
$$\lim_{x \to 0^+}\left(\frac{x}{\sqrt{x + 1}}\right)$$ 
Limit(x/sqrt(1 + x), x, 0)
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
Plot the graph
Rapid solution [src] 
0
$$0$$
Expand and simplify
One‐sided limits [src] 
     /    x    \
 lim |---------|
x->0+|  _______|
     \\/ 1 + x /
$$\lim_{x \to 0^+}\left(\frac{x}{\sqrt{x + 1}}\right)$$ 
0
$$0$$ 
= 1.55921026308246e-29
     /    x    \
 lim |---------|
x->0-|  _______|
     \\/ 1 + x /
$$\lim_{x \to 0^-}\left(\frac{x}{\sqrt{x + 1}}\right)$$ 
0
$$0$$ 
= -1.44283737693697e-33
= -1.44283737693697e-33
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{x}{\sqrt{x + 1}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{\sqrt{x + 1}}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{x}{\sqrt{x + 1}}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{x}{\sqrt{x + 1}}\right) = \frac{\sqrt{2}}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{\sqrt{x + 1}}\right) = \frac{\sqrt{2}}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{\sqrt{x + 1}}\right) = \infty i$$
More at x→-oo
Numerical answer [src] 
1.55921026308246e-29
1.55921026308246e-29
The graph
Limit of the function x/sqrt(1+x)
    © Mister Exam – Calculator