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x*e^(1/x)
Limit of the function/ x*e^(1/x)

Limit of the function x*e^(1/x)

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You have entered [src] 
     /  x ___\
 lim \x*\/ E /
x->0+
lim⁡x→0+(e1xx)\lim_{x \to 0^+}\left(e^{\frac{1}{x}} x\right) 
Limit(x*E^(1/x), x, 0)
The graph
02468-8-6-4-2-10104000-2000
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(e1xx)=∞\lim_{x \to 0^-}\left(e^{\frac{1}{x}} x\right) = \infty
More at x→0 from the left
lim⁡x→0+(e1xx)=∞\lim_{x \to 0^+}\left(e^{\frac{1}{x}} x\right) = \infty
lim⁡x→∞(e1xx)=∞\lim_{x \to \infty}\left(e^{\frac{1}{x}} x\right) = \infty
More at x→oo
lim⁡x→1−(e1xx)=e\lim_{x \to 1^-}\left(e^{\frac{1}{x}} x\right) = e
More at x→1 from the left
lim⁡x→1+(e1xx)=e\lim_{x \to 1^+}\left(e^{\frac{1}{x}} x\right) = e
More at x→1 from the right
lim⁡x→−∞(e1xx)=−∞\lim_{x \to -\infty}\left(e^{\frac{1}{x}} x\right) = -\infty
More at x→-oo
Rapid solution [src] 
oo
∞\infty
Expand and simplify
One‐sided limits [src] 
     /  x ___\
 lim \x*\/ E /
x->0+
lim⁡x→0+(e1xx)\lim_{x \to 0^+}\left(e^{\frac{1}{x}} x\right) 
oo
∞\infty 
= 0.0657325076344887
     /  x ___\
 lim \x*\/ E /
x->0-
lim⁡x→0−(e1xx)\lim_{x \to 0^-}\left(e^{\frac{1}{x}} x\right) 
0
00 
= -2.6502391286206e-28
= -2.6502391286206e-28
Numerical answer [src] 
0.0657325076344887
0.0657325076344887
The graph
Limit of the function x*e^(1/x)
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