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