Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-1+x^4)/(-1+x+x^4-x^3)
- Limit of (2+x^3-3*x)/(-2+x^3-4*x^2+5*x)
-
Limit of (-2+x^3)/(-5+9*x)
-
Limit of (x+x^3-15*x^2)/(15*x+18*x^2)
- Graphing y =:
- 1/(9*x)
-
Identical expressions
- one /(nine *x)
- 1 divide by (9 multiply by x)
- one divide by (nine multiply by x)
- 1/(9x)
- 1/9x
- 1 divide by (9*x)
-
Similar expressions
- 1/(9*x+10*x^2)
- -9+x^2-1/(9*x^2)
Limit of the function 1/(9*x)
The solution
You have entered
[src]
1 lim --- x->oo9*x
$$\lim_{x \to \infty} \frac{1}{9 x}$$
Limit(1/(9*x), x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty} \frac{1}{9 x}$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty} \frac{1}{9 x}$$ =
$$\lim_{x \to \infty}\left(\frac{\frac{1}{9} \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\frac{1}{9} \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(\frac{u}{9}\right)$$
=
$$\frac{0}{9} = 0$$
The final answer:
$$\lim_{x \to \infty} \frac{1}{9 x} = 0$$
$$\lim_{x \to \infty} \frac{1}{9 x}$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty} \frac{1}{9 x}$$ =
$$\lim_{x \to \infty}\left(\frac{\frac{1}{9} \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\frac{1}{9} \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(\frac{u}{9}\right)$$
=
$$\frac{0}{9} = 0$$
The final answer:
$$\lim_{x \to \infty} \frac{1}{9 x} = 0$$
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 x→0, -oo, +oo, 1
$$\lim_{x \to \infty} \frac{1}{9 x} = 0$$
$$\lim_{x \to 0^-} \frac{1}{9 x} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{9 x} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{9 x} = \frac{1}{9}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{9 x} = \frac{1}{9}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{9 x} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \frac{1}{9 x} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{9 x} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{9 x} = \frac{1}{9}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{9 x} = \frac{1}{9}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{9 x} = 0$$
More at x→-oo
The graph