Limit of the function x*sqrt(2-x)

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     /    _______\
 lim \x*\/ 2 - x /
x->oo

\lim_{x \to \infty}\left(x \sqrt{2 - x}\right)

Limit(x*sqrt(2 - 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

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Rapid solution [src]

oo*I

\infty i

Expand and simplify

Other limits x→0, -oo, +oo, 1

\lim_{x \to \infty}\left(x \sqrt{2 - x}\right) = \infty i

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

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

\lim_{x \to 1^-}\left(x \sqrt{2 - x}\right) = 1

\lim_{x \to 1^+}\left(x \sqrt{2 - x}\right) = 1

\lim_{x \to -\infty}\left(x \sqrt{2 - x}\right) = -\infty

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