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