Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (1-3*x^2+2*x^3)/(x^3+2*x+4*x^2)
-
Limit of (-4-7*x+2*x^2)/(4-13*x+3*x^2)
-
Limit of 5+3*n
-
Limit of (-12+x^2-4*x)/(48+x^2-14*x)
-
Identical expressions
- five + three *n
- 5 plus 3 multiply by n
- five plus three multiply by n
- 5+3n
-
Similar expressions
- 5-3*n
Limit of the function 5+3*n
The solution
You have entered
[src]
lim (5 + 3*n) n->oo
$$\lim_{n \to \infty}\left(3 n + 5\right)$$
Limit(5 + 3*n, n, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{n \to \infty}\left(3 n + 5\right)$$
Let's divide numerator and denominator by n:
$$\lim_{n \to \infty}\left(3 n + 5\right)$$ =
$$\lim_{n \to \infty}\left(\frac{3 + \frac{5}{n}}{\frac{1}{n}}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{3 + \frac{5}{n}}{\frac{1}{n}}\right) = \lim_{u \to 0^+}\left(\frac{5 u + 3}{u}\right)$$
=
$$\frac{0 \cdot 5 + 3}{0} = \infty$$
The final answer:
$$\lim_{n \to \infty}\left(3 n + 5\right) = \infty$$
$$\lim_{n \to \infty}\left(3 n + 5\right)$$
Let's divide numerator and denominator by n:
$$\lim_{n \to \infty}\left(3 n + 5\right)$$ =
$$\lim_{n \to \infty}\left(\frac{3 + \frac{5}{n}}{\frac{1}{n}}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{3 + \frac{5}{n}}{\frac{1}{n}}\right) = \lim_{u \to 0^+}\left(\frac{5 u + 3}{u}\right)$$
=
$$\frac{0 \cdot 5 + 3}{0} = \infty$$
The final answer:
$$\lim_{n \to \infty}\left(3 n + 5\right) = \infty$$
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
$$\lim_{n \to \infty}\left(3 n + 5\right) = \infty$$
$$\lim_{n \to 0^-}\left(3 n + 5\right) = 5$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(3 n + 5\right) = 5$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(3 n + 5\right) = 8$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(3 n + 5\right) = 8$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(3 n + 5\right) = -\infty$$
More at n→-oo
$$\lim_{n \to 0^-}\left(3 n + 5\right) = 5$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(3 n + 5\right) = 5$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(3 n + 5\right) = 8$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(3 n + 5\right) = 8$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(3 n + 5\right) = -\infty$$
More at n→-oo
The graph