Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of sin(6*pi*x)/sin(pi*x)
- Limit of cos(x)/factorial(x)
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Limit of asin(1+x)^2/((1+x)*atan(1+x))
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Limit of 4*x/(1+x)
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Identical expressions
- cos(x)/factorial(x)
- co sinus of e of (x) divide by factorial(x)
- cosx/factorialx
- cos(x) divide by factorial(x)
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Similar expressions
- cosx/factorial(x)
Limit of the function cos(x)/factorial(x)
The solution
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/cos(x)\ lim |------| x->oo\ x! /
$$\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)}}{x!}\right)$$
Limit(cos(x)/factorial(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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)}}{x!}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)}}{x!}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{x!}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\cos{\left(x \right)}}{x!}\right) = \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos{\left(x \right)}}{x!}\right) = \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)}}{x!}\right) = \frac{\left\langle -1, 1\right\rangle}{\left(-\infty\right)!}$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)}}{x!}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{x!}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\cos{\left(x \right)}}{x!}\right) = \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos{\left(x \right)}}{x!}\right) = \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)}}{x!}\right) = \frac{\left\langle -1, 1\right\rangle}{\left(-\infty\right)!}$$
More at x→-oo