Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (5+x-3*x^2)/(4-x+2*x^2)
-
Limit of (4-x^2)/(3-x^2)
-
Limit of (3+2*x)/(1-5*x)
-
Limit of (1-2*cos(x))/sin(3*x)
- Integral of d{x}:
- 9+x
- Graphing y =:
- 9+x
-
Identical expressions
- nine +x
- 9 plus x
- nine plus x
-
Similar expressions
- 9-x
Limit of the function 9+x
The solution
You have entered
[src]
lim (9 + x) x->oo
$$\lim_{x \to \infty}\left(x + 9\right)$$
Limit(9 + x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(x + 9\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(x + 9\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{9}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{9}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{9 u + 1}{u}\right)$$
=
$$\frac{0 \cdot 9 + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x + 9\right) = \infty$$
$$\lim_{x \to \infty}\left(x + 9\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(x + 9\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{9}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{9}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{9 u + 1}{u}\right)$$
=
$$\frac{0 \cdot 9 + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x + 9\right) = \infty$$
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 x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(x + 9\right) = \infty$$
$$\lim_{x \to 0^-}\left(x + 9\right) = 9$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x + 9\right) = 9$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x + 9\right) = 10$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x + 9\right) = 10$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x + 9\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x + 9\right) = 9$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x + 9\right) = 9$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x + 9\right) = 10$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x + 9\right) = 10$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x + 9\right) = -\infty$$
More at x→-oo
The graph