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Limit of the function/ x*e^x

Limit of the function x*e^x

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You have entered [src] 
      /   x\
 lim  \x*E /
x->-oo
lim⁡x→−∞(exx)\lim_{x \to -\infty}\left(e^{x} x\right) 
Limit(x*E^x, x, -oo)
Lopital's rule
We have indeterminateness of type
-oo/oo,

i.e. limit for the numerator is
lim⁡x→−∞x=−∞\lim_{x \to -\infty} x = -\infty
and limit for the denominator is
lim⁡x→−∞e−x=∞\lim_{x \to -\infty} e^{- x} = \infty
Let's take derivatives of the numerator and denominator until we eliminate indeterninateness.
lim⁡x→−∞(exx)\lim_{x \to -\infty}\left(e^{x} x\right)
=
Let's transform the function under the limit a few
lim⁡x→−∞(xex)\lim_{x \to -\infty}\left(x e^{x}\right)
=
lim⁡x→−∞(ddxxddxe−x)\lim_{x \to -\infty}\left(\frac{\frac{d}{d x} x}{\frac{d}{d x} e^{- x}}\right)
=
lim⁡x→−∞(−ex)\lim_{x \to -\infty}\left(- e^{x}\right)
=
lim⁡x→−∞(−ex)\lim_{x \to -\infty}\left(- e^{x}\right)
=
00
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
02468-8-6-4-2-1010-250000250000
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→−∞(exx)=0\lim_{x \to -\infty}\left(e^{x} x\right) = 0
lim⁡x→∞(exx)=∞\lim_{x \to \infty}\left(e^{x} x\right) = \infty
More at x→oo
lim⁡x→0−(exx)=0\lim_{x \to 0^-}\left(e^{x} x\right) = 0
More at x→0 from the left
lim⁡x→0+(exx)=0\lim_{x \to 0^+}\left(e^{x} x\right) = 0
More at x→0 from the right
lim⁡x→1−(exx)=e\lim_{x \to 1^-}\left(e^{x} x\right) = e
More at x→1 from the left
lim⁡x→1+(exx)=e\lim_{x \to 1^+}\left(e^{x} x\right) = e
More at x→1 from the right
Rapid solution [src] 
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00
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The graph
Limit of the function x*e^x
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