Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of ((11+7*x+7*x^2)/(14+9*x+13*x^2))^(4*x)
-
Limit of (4-3*x^3+6*x^5)/(1+2*x^4+3*x^5)
-
Limit of 1+19*n/3
-
Limit of (5+3*n)/|-1+3*n|
-
Identical expressions
- one + nineteen *n/ three
- 1 plus 19 multiply by n divide by 3
- one plus nineteen multiply by n divide by three
- 1+19n/3
- 1+19*n divide by 3
-
Similar expressions
- 1-19*n/3
Limit of the function 1+19*n/3
The solution
You have entered
[src]
/ 19*n\ lim |1 + ----| n->oo\ 3 /
$$\lim_{n \to \infty}\left(\frac{19 n}{3} + 1\right)$$
Limit(1 + (19*n)/3, n, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{n \to \infty}\left(\frac{19 n}{3} + 1\right)$$
Let's divide numerator and denominator by n:
$$\lim_{n \to \infty}\left(\frac{19 n}{3} + 1\right)$$ =
$$\lim_{n \to \infty}\left(\frac{\frac{19}{3} + \frac{1}{n}}{\frac{1}{n}}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{\frac{19}{3} + \frac{1}{n}}{\frac{1}{n}}\right) = \lim_{u \to 0^+}\left(\frac{u + \frac{19}{3}}{u}\right)$$
=
$$\frac{19}{0 \cdot 3} = \infty$$
The final answer:
$$\lim_{n \to \infty}\left(\frac{19 n}{3} + 1\right) = \infty$$
$$\lim_{n \to \infty}\left(\frac{19 n}{3} + 1\right)$$
Let's divide numerator and denominator by n:
$$\lim_{n \to \infty}\left(\frac{19 n}{3} + 1\right)$$ =
$$\lim_{n \to \infty}\left(\frac{\frac{19}{3} + \frac{1}{n}}{\frac{1}{n}}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{\frac{19}{3} + \frac{1}{n}}{\frac{1}{n}}\right) = \lim_{u \to 0^+}\left(\frac{u + \frac{19}{3}}{u}\right)$$
=
$$\frac{19}{0 \cdot 3} = \infty$$
The final answer:
$$\lim_{n \to \infty}\left(\frac{19 n}{3} + 1\right) = \infty$$
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
$$\lim_{n \to \infty}\left(\frac{19 n}{3} + 1\right) = \infty$$
$$\lim_{n \to 0^-}\left(\frac{19 n}{3} + 1\right) = 1$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{19 n}{3} + 1\right) = 1$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{19 n}{3} + 1\right) = \frac{22}{3}$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{19 n}{3} + 1\right) = \frac{22}{3}$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{19 n}{3} + 1\right) = -\infty$$
More at n→-oo
$$\lim_{n \to 0^-}\left(\frac{19 n}{3} + 1\right) = 1$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{19 n}{3} + 1\right) = 1$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{19 n}{3} + 1\right) = \frac{22}{3}$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{19 n}{3} + 1\right) = \frac{22}{3}$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{19 n}{3} + 1\right) = -\infty$$
More at n→-oo
The graph