Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of ((3+5*x)/(-2+4*x))^(1+3*x)
-
Limit of (1-2*x+5*x^2)/(-3+x+2*x^2)
-
Limit of (-64+4^x)/(-3+x)
-
Limit of (-7-2*x^2+3*x^4)/(5+3*x+3*x^4)
- Graphing y =:
- 8-x^3
- Integral of d{x}:
- 8-x^3
- Factor polynomial:
- 8-x^3
-
Identical expressions
- eight -x^ three
- 8 minus x cubed
- eight minus x to the power of three
- 8-x3
- 8-x³
- 8-x to the power of 3
-
Similar expressions
- 8+x^3
Limit of the function 8-x^3
The solution
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/ 3\ lim \8 - x / x->oo
$$\lim_{x \to \infty}\left(8 - x^{3}\right)$$
Limit(8 - x^3, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(8 - x^{3}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(8 - x^{3}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{8}{x^{3}}}{\frac{1}{x^{3}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{8}{x^{3}}}{\frac{1}{x^{3}}}\right) = \lim_{u \to 0^+}\left(\frac{8 u^{3} - 1}{u^{3}}\right)$$
=
$$\frac{-1 + 8 \cdot 0^{3}}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(8 - x^{3}\right) = -\infty$$
$$\lim_{x \to \infty}\left(8 - x^{3}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(8 - x^{3}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{8}{x^{3}}}{\frac{1}{x^{3}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{8}{x^{3}}}{\frac{1}{x^{3}}}\right) = \lim_{u \to 0^+}\left(\frac{8 u^{3} - 1}{u^{3}}\right)$$
=
$$\frac{-1 + 8 \cdot 0^{3}}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(8 - x^{3}\right) = -\infty$$
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
$$\lim_{x \to \infty}\left(8 - x^{3}\right) = -\infty$$
$$\lim_{x \to 0^-}\left(8 - x^{3}\right) = 8$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(8 - x^{3}\right) = 8$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(8 - x^{3}\right) = 7$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(8 - x^{3}\right) = 7$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(8 - x^{3}\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(8 - x^{3}\right) = 8$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(8 - x^{3}\right) = 8$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(8 - x^{3}\right) = 7$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(8 - x^{3}\right) = 7$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(8 - x^{3}\right) = \infty$$
More at x→-oo
The graph