Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-2+sqrt(x))/(-4+x^2)
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Limit of (-exp(-x)+exp(x))/(exp(x)+exp(-x))
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Limit of x+2*x^3+5*x^4-x^2/3
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Limit of (-x^3+2*x+5*x^4)/(1+x^4-8*x^3)
- Derivative of:
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2/sqrt(x)
- Integral of d{x}:
- 2/sqrt(x)
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Identical expressions
- two /sqrt(x)
- 2 divide by square root of (x)
- two divide by square root of (x)
- 2/√(x)
- 2/sqrtx
- 2 divide by sqrt(x)
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Similar expressions
- -2+x-sqrt(2)/sqrt(x)
- (-4+x^2)/(sqrt(x)-sqrt(2))
- (x^2-y^2)/sqrt(x^2+y^2)
- y*x^2/sqrt(x^2+y^2)
Limit of the function 2/sqrt(x)
The solution
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[src]
/ 2 \
lim |-----|
x->0+| ___|
\\/ x /
$$\lim_{x \to 0^+}\left(\frac{2}{\sqrt{x}}\right)$$
Limit(2/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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{2}{\sqrt{x}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2}{\sqrt{x}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{2}{\sqrt{x}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{2}{\sqrt{x}}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2}{\sqrt{x}}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2}{\sqrt{x}}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2}{\sqrt{x}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{2}{\sqrt{x}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{2}{\sqrt{x}}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2}{\sqrt{x}}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2}{\sqrt{x}}\right) = 0$$
More at x→-oo
One‐sided limits
[src]
/ 2 \
lim |-----|
x->0+| ___|
\\/ x /
$$\lim_{x \to 0^+}\left(\frac{2}{\sqrt{x}}\right)$$
oo
$$\infty$$
= 24.576411454889
/ 2 \
lim |-----|
x->0-| ___|
\\/ x /
$$\lim_{x \to 0^-}\left(\frac{2}{\sqrt{x}}\right)$$
-oo*I
$$- \infty i$$
= (0.0 - 24.576411454889j)
= (0.0 - 24.576411454889j)
The graph