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2^(-n)*2^(1+n)
Limit of the function/ 2^(-n)*2^(1+n)

Limit of the function 2^(-n)*2^(1+n)

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     / -n  1 + n\
 lim \2  *2     /
n->oo
lim⁡n→∞(2−n2n+1)\lim_{n \to \infty}\left(2^{- n} 2^{n + 1}\right) 
Limit(2^(-n)*2^(1 + n), n, oo, dir='-')
Lopital's rule
We have indeterminateness of type
oo/oo,

i.e. limit for the numerator is
lim⁡n→∞(2⋅2n)=∞\lim_{n \to \infty}\left(2 \cdot 2^{n}\right) = \infty
and limit for the denominator is
lim⁡n→∞2n=∞\lim_{n \to \infty} 2^{n} = \infty
Let's take derivatives of the numerator and denominator until we eliminate indeterninateness.
lim⁡n→∞(2−n2n+1)\lim_{n \to \infty}\left(2^{- n} 2^{n + 1}\right)
=
lim⁡n→∞(ddn2⋅2nddn2n)\lim_{n \to \infty}\left(\frac{\frac{d}{d n} 2 \cdot 2^{n}}{\frac{d}{d n} 2^{n}}\right)
=
lim⁡n→∞2\lim_{n \to \infty} 2
=
lim⁡n→∞2\lim_{n \to \infty} 2
=
22
It can be seen that we have applied Lopital's rule (we have taken derivatives with respect to the numerator and denominator) 1 time(s)
The graph
-0.010-0.008-0.006-0.004-0.0020.0100.0000.0020.0040.0060.0080.00
Plot the graph
Other limits n→0, -oo, +oo, 1
lim⁡n→∞(2−n2n+1)=2\lim_{n \to \infty}\left(2^{- n} 2^{n + 1}\right) = 2
lim⁡n→0−(2−n2n+1)=2\lim_{n \to 0^-}\left(2^{- n} 2^{n + 1}\right) = 2
More at n→0 from the left
lim⁡n→0+(2−n2n+1)=2\lim_{n \to 0^+}\left(2^{- n} 2^{n + 1}\right) = 2
More at n→0 from the right
lim⁡n→1−(2−n2n+1)=2\lim_{n \to 1^-}\left(2^{- n} 2^{n + 1}\right) = 2
More at n→1 from the left
lim⁡n→1+(2−n2n+1)=2\lim_{n \to 1^+}\left(2^{- n} 2^{n + 1}\right) = 2
More at n→1 from the right
lim⁡n→−∞(2−n2n+1)=2\lim_{n \to -\infty}\left(2^{- n} 2^{n + 1}\right) = 2
More at n→-oo
Rapid solution [src] 
2
22
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The graph
Limit of the function 2^(-n)*2^(1+n)
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