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x*2^x*3^(-x)
Limit of the function/ x*2^x*3^(-x)

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x*2^x*3^(-x)

What you mean?

x*2^x/3^x
 
x*2^((x*3)^(-x))
 
x*2^((x*3)^(-x))

Limit of the function x*2^x*3^(-x)

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The solution

You have entered [src] 
     /   x  -x\
 lim \x*2 *3  /
x->oo
lim⁡x→∞(2x3−xx)\lim_{x \to \infty}\left(2^{x} 3^{- x} x\right) 
Limit(x*2^x/3^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
02468-8-6-4-2-1010-1000500
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(2x3−xx)=0\lim_{x \to \infty}\left(2^{x} 3^{- x} x\right) = 0
lim⁡x→0−(2x3−xx)=0\lim_{x \to 0^-}\left(2^{x} 3^{- x} x\right) = 0
More at x→0 from the left
lim⁡x→0+(2x3−xx)=0\lim_{x \to 0^+}\left(2^{x} 3^{- x} x\right) = 0
More at x→0 from the right
lim⁡x→1−(2x3−xx)=23\lim_{x \to 1^-}\left(2^{x} 3^{- x} x\right) = \frac{2}{3}
More at x→1 from the left
lim⁡x→1+(2x3−xx)=23\lim_{x \to 1^+}\left(2^{x} 3^{- x} x\right) = \frac{2}{3}
More at x→1 from the right
lim⁡x→−∞(2x3−xx)=−∞\lim_{x \to -\infty}\left(2^{x} 3^{- x} x\right) = -\infty
More at x→-oo
The graph
Limit of the function x*2^x*3^(-x)
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