Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-12+x^2+4*x)/(-4+x^2)
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Limit of (6+x^2+2*x)/(-1+3*x^2+7*x)
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Limit of (10-51*x+5*x^2)/(-10+x)
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Limit of (1-2*x+5*x^2)/(-3+x+2*x^2)
- Integral of d{x}:
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-x*exp(x)
- Graphing y =:
- -x*exp(x)
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Identical expressions
- -x*exp(x)
- minus x multiply by exponent of (x)
- -xexp(x)
- -xexpx
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Similar expressions
- x*exp(x)
- (x*x^(-x)*exp(x))^(1/x)
Limit of the function -x*exp(x)
The solution
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/ x\ lim \-x*e / x->oo
$$\lim_{x \to \infty}\left(- x e^{x}\right)$$
Limit((-x)*exp(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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(- x e^{x}\right) = -\infty$$
$$\lim_{x \to 0^-}\left(- x e^{x}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x e^{x}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x e^{x}\right) = - e$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x e^{x}\right) = - e$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x e^{x}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- x e^{x}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x e^{x}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x e^{x}\right) = - e$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x e^{x}\right) = - e$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x e^{x}\right) = 0$$
More at x→-oo
The graph