Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of (-3+sqrt(1+4*x))/(-2+x)
-
Limit of x^2+(sqrt(1+3*x)-sqrt(1-2*x))/x
-
Limit of ((11+7*x+7*x^2)/(14+9*x+13*x^2))^(4*x)
-
Limit of (-1+x+6*x^2)/(1/2+x)
- Sum of series:
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-1/n^2
-
Identical expressions
- - one /n^ two
- minus 1 divide by n squared
- minus one divide by n to the power of two
- -1/n2
- -1/n²
- -1/n to the power of 2
- -1 divide by n^2
-
Similar expressions
- 1/n^2
Limit of the function -1/n^2
The solution
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/-1 \
lim |---|
n->oo| 2|
\ n /
$$\lim_{n \to \infty}\left(- \frac{1}{n^{2}}\right)$$
Limit(-1/n^2, n, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{n \to \infty}\left(- \frac{1}{n^{2}}\right)$$
Let's divide numerator and denominator by n^2:
$$\lim_{n \to \infty}\left(- \frac{1}{n^{2}}\right)$$ =
$$\lim_{n \to \infty}\left(\frac{\left(-1\right) \frac{1}{n^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{\left(-1\right) \frac{1}{n^{2}}}{1}\right) = \lim_{u \to 0^+}\left(- u^{2}\right)$$
=
$$- 0^{2} = 0$$
The final answer:
$$\lim_{n \to \infty}\left(- \frac{1}{n^{2}}\right) = 0$$
$$\lim_{n \to \infty}\left(- \frac{1}{n^{2}}\right)$$
Let's divide numerator and denominator by n^2:
$$\lim_{n \to \infty}\left(- \frac{1}{n^{2}}\right)$$ =
$$\lim_{n \to \infty}\left(\frac{\left(-1\right) \frac{1}{n^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{\left(-1\right) \frac{1}{n^{2}}}{1}\right) = \lim_{u \to 0^+}\left(- u^{2}\right)$$
=
$$- 0^{2} = 0$$
The final answer:
$$\lim_{n \to \infty}\left(- \frac{1}{n^{2}}\right) = 0$$
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
The graph
Other limits n→0, -oo, +oo, 1
$$\lim_{n \to \infty}\left(- \frac{1}{n^{2}}\right) = 0$$
$$\lim_{n \to 0^-}\left(- \frac{1}{n^{2}}\right) = -\infty$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(- \frac{1}{n^{2}}\right) = -\infty$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(- \frac{1}{n^{2}}\right) = -1$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(- \frac{1}{n^{2}}\right) = -1$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(- \frac{1}{n^{2}}\right) = 0$$
More at n→-oo
$$\lim_{n \to 0^-}\left(- \frac{1}{n^{2}}\right) = -\infty$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(- \frac{1}{n^{2}}\right) = -\infty$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(- \frac{1}{n^{2}}\right) = -1$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(- \frac{1}{n^{2}}\right) = -1$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(- \frac{1}{n^{2}}\right) = 0$$
More at n→-oo
The graph