Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-2+sqrt(x))/(-4+x^2)
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Limit of (-exp(-x)+exp(x))/(exp(x)+exp(-x))
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Limit of x+2*x^3+5*x^4-x^2/3
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Limit of (-x^3+2*x+5*x^4)/(1+x^4-8*x^3)
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Identical expressions
- (one +n)/|- one +n|
- (1 plus n) divide by module of minus 1 plus n|
- (one plus n) divide by module of minus one plus n|
- 1+n/|-1+n|
- (1+n) divide by |-1+n|
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Similar expressions
- (1+n)/|-1-n|
- (1+n)/|+1+n|
- (1-n)/|-1+n|
Limit of the function (1+n)/|-1+n|
The solution
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/ 1 + n \ lim |--------| n->oo\|-1 + n|/
$$\lim_{n \to \infty}\left(\frac{n + 1}{\left|{n - 1}\right|}\right)$$
Limit((1 + n)/|-1 + n|, n, oo, dir='-')
The graph
Other limits n→0, -oo, +oo, 1
$$\lim_{n \to \infty}\left(\frac{n + 1}{\left|{n - 1}\right|}\right) = 1$$
$$\lim_{n \to 0^-}\left(\frac{n + 1}{\left|{n - 1}\right|}\right) = 1$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{n + 1}{\left|{n - 1}\right|}\right) = 1$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{n + 1}{\left|{n - 1}\right|}\right) = \infty$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{n + 1}{\left|{n - 1}\right|}\right) = \infty$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{n + 1}{\left|{n - 1}\right|}\right) = -1$$
More at n→-oo
$$\lim_{n \to 0^-}\left(\frac{n + 1}{\left|{n - 1}\right|}\right) = 1$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{n + 1}{\left|{n - 1}\right|}\right) = 1$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{n + 1}{\left|{n - 1}\right|}\right) = \infty$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{n + 1}{\left|{n - 1}\right|}\right) = \infty$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{n + 1}{\left|{n - 1}\right|}\right) = -1$$
More at n→-oo
The graph