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

Limit of the function 1/sqrt(x)

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The solution

You have entered [src] 
     /    1  \
 lim |1*-----|
x->0+|    ___|
     \  \/ x /
$$\lim_{x \to 0^+}\left(1 \cdot \frac{1}{\sqrt{x}}\right)$$ 
Limit(1/sqrt(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
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Rapid solution [src] 
oo
$$\infty$$
Expand and simplify
One‐sided limits [src] 
     /    1  \
 lim |1*-----|
x->0+|    ___|
     \  \/ x /
$$\lim_{x \to 0^+}\left(1 \cdot \frac{1}{\sqrt{x}}\right)$$ 
oo
$$\infty$$ 
= 12.2882057274445
     /    1  \
 lim |1*-----|
x->0-|    ___|
     \  \/ x /
$$\lim_{x \to 0^-}\left(1 \cdot \frac{1}{\sqrt{x}}\right)$$ 
-oo*I
$$- \infty i$$ 
= (0.0 - 12.2882057274445j)
= (0.0 - 12.2882057274445j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(1 \cdot \frac{1}{\sqrt{x}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(1 \cdot \frac{1}{\sqrt{x}}\right) = \infty$$
$$\lim_{x \to \infty}\left(1 \cdot \frac{1}{\sqrt{x}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(1 \cdot \frac{1}{\sqrt{x}}\right) = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(1 \cdot \frac{1}{\sqrt{x}}\right) = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(1 \cdot \frac{1}{\sqrt{x}}\right) = 0$$
More at x→-oo
Numerical answer [src] 
12.2882057274445
12.2882057274445
The graph
Limit of the function 1/sqrt(x)
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