Mister Exam
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How to use it?
- Limit of the function:
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Limit of factorial(x)/(1+2*x)
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Limit of 20
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Limit of -10
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Limit of sin(pi/n)
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Identical expressions
- factorial(x)/(one + two *x)
- factorial(x) divide by (1 plus 2 multiply by x)
- factorial(x) divide by (one plus two multiply by x)
- factorial(x)/(1+2x)
- factorialx/1+2x
- factorial(x) divide by (1+2*x)
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Similar expressions
- factorial(x)/(1-2*x)
- x*cos(factorial(x))/(1+2^x)
- factorial(x)/(1+2^x)
Limit of the function factorial(x)/(1+2*x)
The solution
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/ x! \ lim |-------| x->oo\1 + 2*x/
$$\lim_{x \to \infty}\left(\frac{x!}{2 x + 1}\right)$$
Limit(factorial(x)/(1 + 2*x), x, oo, dir='-')
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{x!}{2 x + 1}\right) = \infty$$
$$\lim_{x \to 0^-}\left(\frac{x!}{2 x + 1}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x!}{2 x + 1}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x!}{2 x + 1}\right) = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x!}{2 x + 1}\right) = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x!}{2 x + 1}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{x!}{2 x + 1}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x!}{2 x + 1}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x!}{2 x + 1}\right) = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x!}{2 x + 1}\right) = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x!}{2 x + 1}\right) = 0$$
More at x→-oo
The graph