Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1-3*x^2+2*x^3)/(x^3+2*x+4*x^2)
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Limit of (-4-7*x+2*x^2)/(4-13*x+3*x^2)
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Limit of 5+3*n
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Limit of (-12+x^2-4*x)/(48+x^2-14*x)
- Integral of d{x}:
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x^3*exp(x^2)
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Identical expressions
- x^ three *exp(x^ two)
- x cubed multiply by exponent of (x squared )
- x to the power of three multiply by exponent of (x to the power of two)
- x3*exp(x2)
- x3*expx2
- x³*exp(x²)
- x to the power of 3*exp(x to the power of 2)
- x^3exp(x^2)
- x3exp(x2)
- x3expx2
- x^3expx^2
Limit of the function x^3*exp(x^2)
The solution
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[src]
/ / 2\\
| 3 \x /|
lim \x *e /
x->0+
$$\lim_{x \to 0^+}\left(x^{3} e^{x^{2}}\right)$$
Limit(x^3*exp(x^2), x, 0)
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
One‐sided limits
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/ / 2\\
| 3 \x /|
lim \x *e /
x->0+
$$\lim_{x \to 0^+}\left(x^{3} e^{x^{2}}\right)$$
0
$$0$$
= 1.29673473149388e-29
/ / 2\\
| 3 \x /|
lim \x *e /
x->0-
$$\lim_{x \to 0^-}\left(x^{3} e^{x^{2}}\right)$$
0
$$0$$
= -1.29673473149388e-29
= -1.29673473149388e-29
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(x^{3} e^{x^{2}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{3} e^{x^{2}}\right) = 0$$
$$\lim_{x \to \infty}\left(x^{3} e^{x^{2}}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(x^{3} e^{x^{2}}\right) = e$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{3} e^{x^{2}}\right) = e$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{3} e^{x^{2}}\right) = -\infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{3} e^{x^{2}}\right) = 0$$
$$\lim_{x \to \infty}\left(x^{3} e^{x^{2}}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(x^{3} e^{x^{2}}\right) = e$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{3} e^{x^{2}}\right) = e$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{3} e^{x^{2}}\right) = -\infty$$
More at x→-oo
The graph