Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of log(x)*tan(x)
-
Limit of tan(5*x)
-
Limit of sin(x/3)
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Limit of 2*x/(1+x^2)
- Derivative of:
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2/x^2
- Graphing y =:
- 2/x^2
- Integral of d{x}:
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2/x^2
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Identical expressions
- two /x^ two
- 2 divide by x squared
- two divide by x to the power of two
- 2/x2
- 2/x²
- 2/x to the power of 2
- 2 divide by x^2
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Similar expressions
- tan(x/2)^2/x^2
- tan(3*x)^2/x^2
- log(1-x^2)/x^2
- (1+x+x^2)/(x^2-6*x)
Limit of the function 2/x^2
The solution
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/2 \
lim |--|
x->oo| 2|
\x /
$$\lim_{x \to \infty}\left(\frac{2}{x^{2}}\right)$$
Limit(2/x^2, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{2}{x^{2}}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(\frac{2}{x^{2}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{2 \frac{1}{x^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{2 \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(2 u^{2}\right)$$
=
$$2 \cdot 0^{2} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{2}{x^{2}}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{2}{x^{2}}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(\frac{2}{x^{2}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{2 \frac{1}{x^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{2 \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(2 u^{2}\right)$$
=
$$2 \cdot 0^{2} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{2}{x^{2}}\right) = 0$$
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
$$\lim_{x \to \infty}\left(\frac{2}{x^{2}}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{2}{x^{2}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2}{x^{2}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{2}{x^{2}}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2}{x^{2}}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2}{x^{2}}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{2}{x^{2}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2}{x^{2}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{2}{x^{2}}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2}{x^{2}}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2}{x^{2}}\right) = 0$$
More at x→-oo
The graph