Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
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Limit of ((2+x)/(4+x))^cos(x)
-
Limit of -5-2*x^2+8*x
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Limit of (-9+x^2)/(-27+x^3)
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Limit of 1+7*x+11*x^2/2
- Derivative of:
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5/x^2
- Integral of d{x}:
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5/x^2
- Graphing y =:
- 5/x^2
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Identical expressions
- five /x^ two
- 5 divide by x squared
- five divide by x to the power of two
- 5/x2
- 5/x²
- 5/x to the power of 2
- 5 divide by x^2
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Similar expressions
- sqrt(x^5+5/x^2)
- -5+1/x+5/x^2
- (1-5/x^2)^(x^2)
- (5/x^2)^(x^2)
Limit of the function 5/x^2
The solution
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/5 \
lim |--|
x->oo| 2|
\x /
$$\lim_{x \to \infty}\left(\frac{5}{x^{2}}\right)$$
Limit(5/x^2, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{5}{x^{2}}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(\frac{5}{x^{2}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{5 \frac{1}{x^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{5 \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(5 u^{2}\right)$$
=
$$5 \cdot 0^{2} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{5}{x^{2}}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{5}{x^{2}}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(\frac{5}{x^{2}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{5 \frac{1}{x^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{5 \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(5 u^{2}\right)$$
=
$$5 \cdot 0^{2} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{5}{x^{2}}\right) = 0$$
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
$$\lim_{x \to \infty}\left(\frac{5}{x^{2}}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{5}{x^{2}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{5}{x^{2}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{5}{x^{2}}\right) = 5$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{5}{x^{2}}\right) = 5$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{5}{x^{2}}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{5}{x^{2}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{5}{x^{2}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{5}{x^{2}}\right) = 5$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{5}{x^{2}}\right) = 5$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{5}{x^{2}}\right) = 0$$
More at x→-oo
The graph