Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (9+3*x^2+4*x)/(7-7*x+3*x^2)
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Limit of -pi+(1+cos(x))/x
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Limit of (1-5*x)^(1/x)
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Limit of (1+2/n)^(4*n)
- Derivative of:
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sqrt(2+x^2)
- Integral of d{x}:
- sqrt(2+x^2)
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Identical expressions
- sqrt(two +x^ two)
- square root of (2 plus x squared )
- square root of (two plus x to the power of two)
- √(2+x^2)
- sqrt(2+x2)
- sqrt2+x2
- sqrt(2+x²)
- sqrt(2+x to the power of 2)
- sqrt2+x^2
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Similar expressions
- (-5*x^2+3*sqrt(2+x^2))/(x-sqrt(1+x^4-x))
- sqrt(2-x^2)
Limit of the function sqrt(2+x^2)
The solution
You have entered
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lim \/ 2 + x
x->0+
$$\lim_{x \to 0^+} \sqrt{x^{2} + 2}$$
Limit(sqrt(2 + x^2), 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
$$\lim_{x \to 0^-} \sqrt{x^{2} + 2} = \sqrt{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sqrt{x^{2} + 2} = \sqrt{2}$$
$$\lim_{x \to \infty} \sqrt{x^{2} + 2} = \infty$$
More at x→oo
$$\lim_{x \to 1^-} \sqrt{x^{2} + 2} = \sqrt{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sqrt{x^{2} + 2} = \sqrt{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sqrt{x^{2} + 2} = \infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \sqrt{x^{2} + 2} = \sqrt{2}$$
$$\lim_{x \to \infty} \sqrt{x^{2} + 2} = \infty$$
More at x→oo
$$\lim_{x \to 1^-} \sqrt{x^{2} + 2} = \sqrt{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sqrt{x^{2} + 2} = \sqrt{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sqrt{x^{2} + 2} = \infty$$
More at x→-oo
One‐sided limits
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lim \/ 2 + x
x->0+
$$\lim_{x \to 0^+} \sqrt{x^{2} + 2}$$
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$$\sqrt{2}$$
= 1.4142135623731
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lim \/ 2 + x
x->0-
$$\lim_{x \to 0^-} \sqrt{x^{2} + 2}$$
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$$\sqrt{2}$$
= 1.4142135623731
= 1.4142135623731
The graph