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2 years ago

What does positive correlation mean?

2 answers:

5 0

Positive correlation is a relationship between two variables in which both variables move in tandem—that is, in the same direction. A positive correlation exists when one variable decreases as the other variable decreases, or one variable increases while the other increases.

valina [46]2 years ago

4 0

Answer:A positive correlation is a relationship between two variables such that their values increase or decrease together.

Step-by-step explanation:

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mr_godi [17]

Rationalize both the numerator and denominator. Given

$\dfrac{\sqrt a-\sqrt b}{\sqrt c-\sqrt d}$

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$\dfrac{\sqrt a-\sqrt b}{\sqrt c-\sqrt d} \cdot \dfrac{\sqrt a+\sqrt b}{\sqrt a+\sqrt b} \cdot \dfrac{\sqrt c+\sqrt d}{\sqrt c+\sqrt d} \\\\ = \dfrac{\left(\sqrt a\right)^2 - \left(\sqrt b\right)^2}{\left(\sqrt c\right)^2-\left(\sqrt d\right)^2} \cdot \dfrac{\sqrt c+\sqrt d}{\sqrt a + \sqrt b} \\\\ = \dfrac{a-b}{c-d} \cdot \dfrac{\sqrt c+\sqrt d}{\sqrt a + \sqrt b}$

Then the limit is equivalent to

$\displaystyle \lim_{n\to\infty} \frac{(n+3)-n}{(n+1)-n} \cdot \dfrac{\sqrt{n+1}+\sqrt n}{\sqrt{n+3}+\sqrt n} = 3 \lim_{n\to\infty} \dfrac{\sqrt{n+1}+\sqrt n}{\sqrt{n+3}+\sqrt n}$

For the remaining expression, divide through uniformly by $\sqrt n$ :

$\dfrac{\sqrt{n+1}+\sqrt n}{\sqrt{n+3}+\sqrt n} = \dfrac{\sqrt{1+\frac1n} + 1}{\sqrt{1+\frac3n}+1}$

As <em>n</em> goes to infinity, the remaining terms containing <em>n</em> converge to 0, leaving

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making the overall limit 3.

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