Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 2+((-1+x)/(3+x))^x
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Limit of (-1+x)/(x+x^2)
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Limit of ((1+x)^4-(-1+x)^4)/((1+x)^4+(-1+x)^4)
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Limit of tan(6*x)/(3*x)
- Integral of d{x}:
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sqrt(5+x^2)
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Identical expressions
- sqrt(five +x^ two)
- square root of (5 plus x squared )
- square root of (five plus x to the power of two)
- √(5+x^2)
- sqrt(5+x2)
- sqrt5+x2
- sqrt(5+x²)
- sqrt(5+x to the power of 2)
- sqrt5+x^2
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Similar expressions
- sqrt(5-x^2)
Limit of the function sqrt(5+x^2)
The solution
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lim \/ 5 + x
x->oo
$$\lim_{x \to \infty} \sqrt{x^{2} + 5}$$
Limit(sqrt(5 + 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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty} \sqrt{x^{2} + 5} = \infty$$
$$\lim_{x \to 0^-} \sqrt{x^{2} + 5} = \sqrt{5}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sqrt{x^{2} + 5} = \sqrt{5}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sqrt{x^{2} + 5} = \sqrt{6}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sqrt{x^{2} + 5} = \sqrt{6}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sqrt{x^{2} + 5} = \infty$$
More at x→-oo
$$\lim_{x \to 0^-} \sqrt{x^{2} + 5} = \sqrt{5}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sqrt{x^{2} + 5} = \sqrt{5}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sqrt{x^{2} + 5} = \sqrt{6}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sqrt{x^{2} + 5} = \sqrt{6}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sqrt{x^{2} + 5} = \infty$$
More at x→-oo
The graph