Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of x^2*(1/3-cos(8*x)/3)
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Limit of (-2+x^2-x)/(-2+x+3*x^2)
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Limit of (-1+sin(x))/cos(x)
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Limit of (-2*sin(x)+sin(2*x))/(x*log(cos(5*x)))
- Graphing y =:
- sqrt(x)+sqrt(4-x)
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Identical expressions
- sqrt(x)+sqrt(four -x)
- square root of (x) plus square root of (4 minus x)
- square root of (x) plus square root of (four minus x)
- √(x)+√(4-x)
- sqrtx+sqrt4-x
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Similar expressions
- sqrt(x)-sqrt(4-x)
- sqrt(x)+sqrt(4+x)
Limit of the function sqrt(x)+sqrt(4-x)
The solution
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/ ___ _______\ lim \\/ x + \/ 4 - x / x->oo
$$\lim_{x \to \infty}\left(\sqrt{x} + \sqrt{4 - x}\right)$$
Limit(sqrt(x) + sqrt(4 - x), 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
$$\lim_{x \to \infty}\left(\sqrt{x} + \sqrt{4 - x}\right) = \infty \operatorname{sign}{\left(1 + i \right)}$$
$$\lim_{x \to 0^-}\left(\sqrt{x} + \sqrt{4 - x}\right) = 2$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sqrt{x} + \sqrt{4 - x}\right) = 2$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\sqrt{x} + \sqrt{4 - x}\right) = 1 + \sqrt{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sqrt{x} + \sqrt{4 - x}\right) = 1 + \sqrt{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sqrt{x} + \sqrt{4 - x}\right) = \infty \operatorname{sign}{\left(1 + i \right)}$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\sqrt{x} + \sqrt{4 - x}\right) = 2$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sqrt{x} + \sqrt{4 - x}\right) = 2$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\sqrt{x} + \sqrt{4 - x}\right) = 1 + \sqrt{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sqrt{x} + \sqrt{4 - x}\right) = 1 + \sqrt{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sqrt{x} + \sqrt{4 - x}\right) = \infty \operatorname{sign}{\left(1 + i \right)}$$
More at x→-oo