Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of -cos(x)+5*x
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Limit of (-30+x^2-x)/(125+x^3)
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Limit of sin(9*x)
- Limit of cot(pi*x)
- Integral of d{x}:
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x*exp(x^2/2)
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Identical expressions
- x*exp(x^ two / two)
- x multiply by exponent of (x squared divide by 2)
- x multiply by exponent of (x to the power of two divide by two)
- x*exp(x2/2)
- x*expx2/2
- x*exp(x²/2)
- x*exp(x to the power of 2/2)
- xexp(x^2/2)
- xexp(x2/2)
- xexpx2/2
- xexpx^2/2
- x*exp(x^2 divide by 2)
Limit of the function x*exp(x^2/2)
The solution
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lim \x*e /
x->-oo
$$\lim_{x \to -\infty}\left(x e^{\frac{x^{2}}{2}}\right)$$
Limit(x*exp(x^2/2), x, -oo)
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
$$\lim_{x \to -\infty}\left(x e^{\frac{x^{2}}{2}}\right) = -\infty$$
$$\lim_{x \to \infty}\left(x e^{\frac{x^{2}}{2}}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(x e^{\frac{x^{2}}{2}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x e^{\frac{x^{2}}{2}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x e^{\frac{x^{2}}{2}}\right) = e^{\frac{1}{2}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x e^{\frac{x^{2}}{2}}\right) = e^{\frac{1}{2}}$$
More at x→1 from the right
$$\lim_{x \to \infty}\left(x e^{\frac{x^{2}}{2}}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(x e^{\frac{x^{2}}{2}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x e^{\frac{x^{2}}{2}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x e^{\frac{x^{2}}{2}}\right) = e^{\frac{1}{2}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x e^{\frac{x^{2}}{2}}\right) = e^{\frac{1}{2}}$$
More at x→1 from the right
The graph