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2^x*2^(-1-x)

2^x*2^(-1 - x)

2^((x*2)^(-1 - x))

2^((x*2)^(-1 - x))

Limit of the function 2^x*2^(-1-x)

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     / x  -1 - x\
 lim \2 *2      /
x->oo

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

Limit(2^x*2^(-1 - 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

Rapid solution [src]

1/2

\frac{1}{2}

Expand and simplify

Other limits x→0, -oo, +oo, 1

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

\lim_{x \to 0^-}\left(2^{x} 2^{- x - 1}\right) = \frac{1}{2}

\lim_{x \to 0^+}\left(2^{x} 2^{- x - 1}\right) = \frac{1}{2}

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

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

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