Mister Exam
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How to use it?
- Limit of the function:
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Limit of cos(x^2)
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Limit of (-sin(x)+cos(x))^(1/x)
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Limit of (cos(x)/cosh(x))^(1/(x*log(1+x)))
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Limit of (-1+cos(x))*cot(x)
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Identical expressions
- n*x*(n+x)
- n multiply by x multiply by (n plus x)
- nx(n+x)
- nxn+x
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Similar expressions
- n*x*(n-x)
Limit of the function n*x*(n+x)
The solution
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lim (n*x*(n + x)) x->oo
$$\lim_{x \to \infty}\left(n x \left(n + x\right)\right)$$
Limit((n*x)*(n + 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
$$\lim_{x \to \infty}\left(n x \left(n + x\right)\right) = \infty \operatorname{sign}{\left(n \right)}$$
$$\lim_{x \to 0^-}\left(n x \left(n + x\right)\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(n x \left(n + x\right)\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(n x \left(n + x\right)\right) = n^{2} + n$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(n x \left(n + x\right)\right) = n^{2} + n$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(n x \left(n + x\right)\right) = \infty \operatorname{sign}{\left(n \right)}$$
More at x→-oo
$$\lim_{x \to 0^-}\left(n x \left(n + x\right)\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(n x \left(n + x\right)\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(n x \left(n + x\right)\right) = n^{2} + n$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(n x \left(n + x\right)\right) = n^{2} + n$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(n x \left(n + x\right)\right) = \infty \operatorname{sign}{\left(n \right)}$$
More at x→-oo