Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
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Limit of (-2+x)/(-2+x^2-x)
-
Limit of cos(5*x)*sin(2*x)/tan(x)
-
Limit of 3*sin(x)^2/(4*x)
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Limit of log(1+e^x)
- Integral of d{x}:
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8/x^2
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Identical expressions
- eight /x^ two
- 8 divide by x squared
- eight divide by x to the power of two
- 8/x2
- 8/x²
- 8/x to the power of 2
- 8 divide by x^2
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Similar expressions
- 28/(x^2+14*x)
Limit of the function 8/x^2
The solution
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/8 \
lim |--|
x->oo| 2|
\x /
$$\lim_{x \to \infty}\left(\frac{8}{x^{2}}\right)$$
Limit(8/x^2, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{8}{x^{2}}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(\frac{8}{x^{2}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{8 \frac{1}{x^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{8 \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(8 u^{2}\right)$$
=
$$8 \cdot 0^{2} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{8}{x^{2}}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{8}{x^{2}}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(\frac{8}{x^{2}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{8 \frac{1}{x^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{8 \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(8 u^{2}\right)$$
=
$$8 \cdot 0^{2} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{8}{x^{2}}\right) = 0$$
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
$$\lim_{x \to \infty}\left(\frac{8}{x^{2}}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{8}{x^{2}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{8}{x^{2}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{8}{x^{2}}\right) = 8$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{8}{x^{2}}\right) = 8$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{8}{x^{2}}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{8}{x^{2}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{8}{x^{2}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{8}{x^{2}}\right) = 8$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{8}{x^{2}}\right) = 8$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{8}{x^{2}}\right) = 0$$
More at x→-oo
The graph