Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
- Limit of x^x/factorial(2*x)
-
Limit of x*tan(4*x)/(1-cos(x))
-
Limit of x*(-log(6+x)+log(x))
-
Limit of x/(3+7*x)
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Identical expressions
- x^x/factorial(two *x)
- x to the power of x divide by factorial(2 multiply by x)
- x to the power of x divide by factorial(two multiply by x)
- xx/factorial(2*x)
- xx/factorial2*x
- x^x/factorial(2x)
- xx/factorial(2x)
- xx/factorial2x
- x^x/factorial2x
- x^x divide by factorial(2*x)
Limit of the function x^x/factorial(2*x)
The solution
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/ x \
| x |
lim |------|
x->oo\(2*x)!/
$$\lim_{x \to \infty}\left(\frac{x^{x}}{\left(2 x\right)!}\right)$$
Limit(x^x/factorial(2*x), x, oo, dir='-')
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{x^{x}}{\left(2 x\right)!}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{x^{x}}{\left(2 x\right)!}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{x}}{\left(2 x\right)!}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{x}}{\left(2 x\right)!}\right) = \frac{1}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{x}}{\left(2 x\right)!}\right) = \frac{1}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{x}}{\left(2 x\right)!}\right) = \frac{\infty}{\left(-\infty\right)!}$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{x^{x}}{\left(2 x\right)!}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{x}}{\left(2 x\right)!}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{x}}{\left(2 x\right)!}\right) = \frac{1}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{x}}{\left(2 x\right)!}\right) = \frac{1}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{x}}{\left(2 x\right)!}\right) = \frac{\infty}{\left(-\infty\right)!}$$
More at x→-oo