Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of ((-4+3*x)/(2+3*x))^(1+x)/3
-
Limit of (-16+2^x)/(-1+5*sqrt(x)*(5-x))
-
Limit of (-14+x^2-5*x)/(-6+x+2*x^2)
-
Limit of (3+x^2+4*x)/(1+x^3)
- Derivative of:
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x*e^(-x^2)
- Integral of d{x}:
-
x*e^(-x^2)
- Graphing y =:
- x*e^(-x^2)
-
Identical expressions
- x*e^(-x^ two)
- x multiply by e to the power of ( minus x squared )
- x multiply by e to the power of ( minus x to the power of two)
- x*e(-x2)
- x*e-x2
- x*e^(-x²)
- x*e to the power of (-x to the power of 2)
- xe^(-x^2)
- xe(-x2)
- xe-x2
- xe^-x^2
-
Similar expressions
- x*e^(x^2)
Limit of the function x*e^(-x^2)
The solution
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lim \x*E /
x->oo
$$\lim_{x \to \infty}\left(e^{- x^{2}} x\right)$$
Limit(x*E^(-x^2), x, oo, dir='-')
Lopital's rule
We have indeterminateness of type
i.e. limit for the numerator is
$$\lim_{x \to \infty} x = \infty$$
and limit for the denominator is
$$\lim_{x \to \infty} e^{x^{2}} = \infty$$
Let's take derivatives of the numerator and denominator until we eliminate indeterninateness.
$$\lim_{x \to \infty}\left(e^{- x^{2}} x\right)$$
=
Let's transform the function under the limit a few
$$\lim_{x \to \infty}\left(x e^{- x^{2}}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{\frac{d}{d x} x}{\frac{d}{d x} e^{x^{2}}}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{e^{- x^{2}}}{2 x}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{e^{- x^{2}}}{2 x}\right)$$
=
$$0$$
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)
oo/oo,
i.e. limit for the numerator is
$$\lim_{x \to \infty} x = \infty$$
and limit for the denominator is
$$\lim_{x \to \infty} e^{x^{2}} = \infty$$
Let's take derivatives of the numerator and denominator until we eliminate indeterninateness.
$$\lim_{x \to \infty}\left(e^{- x^{2}} x\right)$$
=
Let's transform the function under the limit a few
$$\lim_{x \to \infty}\left(x e^{- x^{2}}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{\frac{d}{d x} x}{\frac{d}{d x} e^{x^{2}}}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{e^{- x^{2}}}{2 x}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{e^{- x^{2}}}{2 x}\right)$$
=
$$0$$
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(e^{- x^{2}} x\right) = 0$$
$$\lim_{x \to 0^-}\left(e^{- x^{2}} x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(e^{- x^{2}} x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(e^{- x^{2}} x\right) = e^{-1}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(e^{- x^{2}} x\right) = e^{-1}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(e^{- x^{2}} x\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(e^{- x^{2}} x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(e^{- x^{2}} x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(e^{- x^{2}} x\right) = e^{-1}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(e^{- x^{2}} x\right) = e^{-1}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(e^{- x^{2}} x\right) = 0$$
More at x→-oo
The graph