Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (2-2*x^3+7*x^4)/(3+x^4)
-
Limit of ((3+5*x)/(-2+4*x))^(1+3*x)
-
Limit of (-64+4^x)/(-3+x)
-
Limit of 4/(9*x)
-
Identical expressions
- four /(nine *x)
- 4 divide by (9 multiply by x)
- four divide by (nine multiply by x)
- 4/(9x)
- 4/9x
- 4 divide by (9*x)
Limit of the function 4/(9*x)
The solution
You have entered
[src]
/ 4 \ lim |---| x->oo\9*x/
$$\lim_{x \to \infty}\left(\frac{4}{9 x}\right)$$
Limit(4/((9*x)), x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{4}{9 x}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{4}{9 x}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{\frac{4}{9} \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\frac{4}{9} \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(\frac{4 u}{9}\right)$$
=
$$\frac{0 \cdot 4}{9} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{4}{9 x}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{4}{9 x}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{4}{9 x}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{\frac{4}{9} \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\frac{4}{9} \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(\frac{4 u}{9}\right)$$
=
$$\frac{0 \cdot 4}{9} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{4}{9 x}\right) = 0$$
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
$$\lim_{x \to \infty}\left(\frac{4}{9 x}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{4}{9 x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{4}{9 x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{4}{9 x}\right) = \frac{4}{9}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{4}{9 x}\right) = \frac{4}{9}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{4}{9 x}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{4}{9 x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{4}{9 x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{4}{9 x}\right) = \frac{4}{9}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{4}{9 x}\right) = \frac{4}{9}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{4}{9 x}\right) = 0$$
More at x→-oo
The graph