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PolarNik [594]
3 years ago
6

0.27=_ hundredthsplease help me​

Mathematics
2 answers:
Cloud [144]3 years ago
5 0

Answer:

27

Step-by-step explanation:

First decimal is tenths, then hundredths, then thousandths and so on

Alexeev081 [22]3 years ago
4 0

Answer:

27 hundredths

Step-by-step explanation:

.2 is in the tenths place,

.07 is in the hundredth place,

.27 is 27 hundredths

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Step-by-step explanation:

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Calculate: ㅤ <img src="https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Crightarrow%20%2B%5Cinfty%7Dx%28%5Csqrt%7Bx%5E%7B2%7D-1%7D-x%29"
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Answer:

\displaystyle \large \boxed{ \lim_{x \rightarrow +\infty} {x\left(\sqrt{x^2-1}-x\right)}=-\dfrac{1}{2}}

Step-by-step explanation:

Hello, please consider the following.

\sqrt{(x^2-1)}-x\\\\=\sqrt{x^2(1-\dfrac{1}{x^2})}-x\\\\=x\left( \sqrt{1-\frac{1}{x^2}}-1\right)

For x close to 0, we can write

\sqrt{1+x}=1+\dfrac{1}{2}x-\dfrac{1}{8}x^2+o(x^2)\\\\\ \text{x tends to } +\infty \text{ means }\dfrac{1}{x} \text{ tends to 0}\\\\\text{So, when }\dfrac{1}{x}\text{  is close to 0, we can write.}\\\\\sqrt{1-\dfrac{1}{x^2}}=1-\dfrac{1}{2}\dfrac{1}{x^2}-\dfrac{1}{8}\dfrac{1}{x^4}+o(\dfrac{1}{x^4})

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x\left( \sqrt{1-\frac{1}{x^2}}-1\right)\\\\=x(1-\dfrac{1}{2}\dfrac{1}{x^2}+o(\dfrac{1}{x^2})-1)\\\\=-\dfrac{1}{2x}+o(\dfrac{1}{x})

It means that

\displaystyle \lim_{x \rightarrow +\infty} {x\left(\sqrt{x^2-1}-x\right)}\\\\=\lim_{x \rightarrow +\infty} {-\dfrac{x}{2x}}=-\dfrac{1}{2}

Thank you

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