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Shalnov [3]
4 years ago
13

Select the proper order from least to greatest for 2⁄3, 7⁄6 , 1⁄8 , 9⁄10 . 

Mathematics
2 answers:
tangare [24]4 years ago
7 0
C. 1/8, 2/3, 9/10, 7/6
Natasha_Volkova [10]4 years ago
5 0
Hello!

To order fractions from least to greatest, change the fractions so that they have a common denominator:120

\frac{2 \times 40}{3 \times 40} =   \frac{80}{120}

\frac{7 \times 20}{6 \times 20} =  \frac{140}{120}

\frac{1 \times 15}{8 \times 15} =  \frac{15}{120}

\frac{9 \times 12}{10 \times 12} =  \frac{108}{120}

<em>Order the fractions

</em>\frac{1}{8},  \frac{2}{3},  \frac{9}{10},  \frac{7}{6}
<em>
I hope you find this useful! :)</em>
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The notation \lim_{x \to 2^{+}}f(x) means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.

So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc

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Part B

Because \lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x) this means that the limit \lim_{x \to 2}f(x) does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

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Part C

You'll follow the same type of steps shown in part A.

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As mentioned earlier, since \lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3, this means the limit \lim_{x \to 4}f(x) does exist and it's equal to 3.

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