Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of (-2+2*x^2+log(x))/(e^x-e)
-
Limit of (-x^2+4*x)/(2-sqrt(x))
-
Limit of ((2+3*x)/(-1+3*x))^(-1+4*x)
-
Limit of (3-x+2*x^2)/(5+x^3-8*x)
- Graphing y =:
- pi-x
- Integral of d{x}:
- pi-x
-
Identical expressions
- pi-x
- Pi minus x
-
Similar expressions
- pi+x
Limit of the function pi-x
The solution
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lim (pi - x) x->-oo
$$\lim_{x \to -\infty}\left(\pi - x\right)$$
Limit(pi - x, x, -oo)
Detail solution
Let's take the limit
$$\lim_{x \to -\infty}\left(\pi - x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to -\infty}\left(\pi - x\right)$$ =
$$\lim_{x \to -\infty}\left(\frac{-1 + \frac{\pi}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to -\infty}\left(\frac{-1 + \frac{\pi}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{\pi u - 1}{u}\right)$$
=
$$\frac{-1 + 0 \pi}{0} = \infty$$
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:
$$\lim_{x \to -\infty}\left(\pi - x\right)$$ =
$$\lim_{x \to -\infty}\left(\frac{-1 + \frac{\pi}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to -\infty}\left(\frac{-1 + \frac{\pi}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{\pi u - 1}{u}\right)$$
=
$$\frac{-1 + 0 \pi}{0} = \infty$$
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
$$\lim_{x \to -\infty}\left(\pi - x\right) = \infty$$
$$\lim_{x \to \infty}\left(\pi - x\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\pi - x\right) = \pi$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\pi - x\right) = \pi$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\pi - x\right) = -1 + \pi$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\pi - x\right) = -1 + \pi$$
More at x→1 from the right
$$\lim_{x \to \infty}\left(\pi - x\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\pi - x\right) = \pi$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\pi - x\right) = \pi$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\pi - x\right) = -1 + \pi$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\pi - x\right) = -1 + \pi$$
More at x→1 from the right
The graph