Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (1+x^2+9*x)/(-5+2*x+7*x^2)
-
Limit of (-tan(2*x)+sin(2*x))/x^3
-
Limit of 3/n^4
-
Limit of (1-cos(x)^2)/(x^2*sin(x)^2)
-
Identical expressions
- three /n^ four
- 3 divide by n to the power of 4
- three divide by n to the power of four
- 3/n4
- 3/n⁴
- 3 divide by n^4
Limit of the function 3/n^4
The solution
You have entered
[src]
/3 \
lim |--|
n->oo| 4|
\n /
$$\lim_{n \to \infty}\left(\frac{3}{n^{4}}\right)$$
Limit(3/n^4, n, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{n \to \infty}\left(\frac{3}{n^{4}}\right)$$
Let's divide numerator and denominator by n^4:
$$\lim_{n \to \infty}\left(\frac{3}{n^{4}}\right)$$ =
$$\lim_{n \to \infty}\left(\frac{3 \frac{1}{n^{4}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{3 \frac{1}{n^{4}}}{1}\right) = \lim_{u \to 0^+}\left(3 u^{4}\right)$$
=
$$3 \cdot 0^{4} = 0$$
The final answer:
$$\lim_{n \to \infty}\left(\frac{3}{n^{4}}\right) = 0$$
$$\lim_{n \to \infty}\left(\frac{3}{n^{4}}\right)$$
Let's divide numerator and denominator by n^4:
$$\lim_{n \to \infty}\left(\frac{3}{n^{4}}\right)$$ =
$$\lim_{n \to \infty}\left(\frac{3 \frac{1}{n^{4}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{3 \frac{1}{n^{4}}}{1}\right) = \lim_{u \to 0^+}\left(3 u^{4}\right)$$
=
$$3 \cdot 0^{4} = 0$$
The final answer:
$$\lim_{n \to \infty}\left(\frac{3}{n^{4}}\right) = 0$$
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
$$\lim_{n \to \infty}\left(\frac{3}{n^{4}}\right) = 0$$
$$\lim_{n \to 0^-}\left(\frac{3}{n^{4}}\right) = \infty$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{3}{n^{4}}\right) = \infty$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{3}{n^{4}}\right) = 3$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{3}{n^{4}}\right) = 3$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{3}{n^{4}}\right) = 0$$
More at n→-oo
$$\lim_{n \to 0^-}\left(\frac{3}{n^{4}}\right) = \infty$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{3}{n^{4}}\right) = \infty$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{3}{n^{4}}\right) = 3$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{3}{n^{4}}\right) = 3$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{3}{n^{4}}\right) = 0$$
More at n→-oo
The graph