Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of 1+4/x
-
Limit of (-6+x^2-x)/(4-x^2)
-
Limit of (-2+x^2-x)/(1+x^2)
-
Limit of 15+x^2-8*x
- Integral of d{x}:
- x/9
- Graphing y =:
- x/9
-
Identical expressions
- x/ nine
- x divide by 9
- x divide by nine
-
Similar expressions
- x/(9-x)
- (-15+x^2+2*x)/(9-x^2)
- sin(4*x)/(9*x^2)
- (-1+sqrt(-2+x))/(9-x^2)
- (-18+x^2+3*x)/(9+x^2)
Limit of the function x/9
The solution
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/x\ lim |-| x->oo\9/
$$\lim_{x \to \infty}\left(\frac{x}{9}\right)$$
Limit(x/9, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{x}{9}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{x}{9}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{9 \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{9 \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{1}{9 u}\right)$$
=
$$\frac{1}{0 \cdot 9} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{x}{9}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{x}{9}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{x}{9}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{9 \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{9 \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{1}{9 u}\right)$$
=
$$\frac{1}{0 \cdot 9} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{x}{9}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(\frac{x}{9}\right) = \infty$$
$$\lim_{x \to 0^-}\left(\frac{x}{9}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{9}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x}{9}\right) = \frac{1}{9}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{9}\right) = \frac{1}{9}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{9}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{x}{9}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{9}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x}{9}\right) = \frac{1}{9}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{9}\right) = \frac{1}{9}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{9}\right) = -\infty$$
More at x→-oo
The graph