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Limit of the function sqrt(x)+sqrt(4-x)

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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

Plot the graph

Rapid solution [src]

oo*sign(1 + I)

\infty \operatorname{sign}{\left(1 + i \right)}

Expand and simplify

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

\lim_{x \to 0^+}\left(\sqrt{x} + \sqrt{4 - x}\right) = 2

\lim_{x \to 1^-}\left(\sqrt{x} + \sqrt{4 - x}\right) = 1 + \sqrt{3}

\lim_{x \to 1^+}\left(\sqrt{x} + \sqrt{4 - x}\right) = 1 + \sqrt{3}

\lim_{x \to -\infty}\left(\sqrt{x} + \sqrt{4 - x}\right) = \infty \operatorname{sign}{\left(1 + i \right)}