Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (1+x^2+9*x)/(-5+2*x+7*x^2)
-
Limit of (-tan(2*x)+sin(2*x))/x^3
-
Limit of 3/n^4
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Limit of (1-cos(x)^2)/(x^2*sin(x)^2)
- Derivative of:
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9/x^2
- Graphing y =:
- 9/x^2
- Integral of d{x}:
- 9/x^2
-
Identical expressions
- nine /x^ two
- 9 divide by x squared
- nine divide by x to the power of two
- 9/x2
- 9/x²
- 9/x to the power of 2
- 9 divide by x^2
Limit of the function 9/x^2
The solution
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/9 \
lim |--|
x->oo| 2|
\x /
$$\lim_{x \to \infty}\left(\frac{9}{x^{2}}\right)$$
Limit(9/x^2, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{9}{x^{2}}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(\frac{9}{x^{2}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{9 \frac{1}{x^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{9 \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(9 u^{2}\right)$$
=
$$9 \cdot 0^{2} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{9}{x^{2}}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{9}{x^{2}}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(\frac{9}{x^{2}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{9 \frac{1}{x^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{9 \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(9 u^{2}\right)$$
=
$$9 \cdot 0^{2} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{9}{x^{2}}\right) = 0$$
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
$$\lim_{x \to \infty}\left(\frac{9}{x^{2}}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{9}{x^{2}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{9}{x^{2}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{9}{x^{2}}\right) = 9$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{9}{x^{2}}\right) = 9$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{9}{x^{2}}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{9}{x^{2}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{9}{x^{2}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{9}{x^{2}}\right) = 9$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{9}{x^{2}}\right) = 9$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{9}{x^{2}}\right) = 0$$
More at x→-oo
The graph