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x*e^(2*x)
Limit of the function/ x*e^(2*x)

Limit of the function x*e^(2*x)

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The solution

You have entered [src] 
     /   2*x\
 lim \x*E   /
x->oo
lim⁡x→∞(e2xx)\lim_{x \to \infty}\left(e^{2 x} x\right) 
Limit(x*E^(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
02468-8-6-4-2-1010-50000000005000000000
Plot the graph
Rapid solution [src] 
oo
∞\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(e2xx)=∞\lim_{x \to \infty}\left(e^{2 x} x\right) = \infty
lim⁡x→0−(e2xx)=0\lim_{x \to 0^-}\left(e^{2 x} x\right) = 0
More at x→0 from the left
lim⁡x→0+(e2xx)=0\lim_{x \to 0^+}\left(e^{2 x} x\right) = 0
More at x→0 from the right
lim⁡x→1−(e2xx)=e2\lim_{x \to 1^-}\left(e^{2 x} x\right) = e^{2}
More at x→1 from the left
lim⁡x→1+(e2xx)=e2\lim_{x \to 1^+}\left(e^{2 x} x\right) = e^{2}
More at x→1 from the right
lim⁡x→−∞(e2xx)=0\lim_{x \to -\infty}\left(e^{2 x} x\right) = 0
More at x→-oo
The graph
Limit of the function x*e^(2*x)
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