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How do I isolate the x in this expression? (ie. so x is by itself). In other words, how do I factor that fraction out?
 one year ago
 one year ago
How do I isolate the x in this expression? (ie. so x is by itself). In other words, how do I factor that fraction out?
 one year ago
 one year ago

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Study23Best ResponseYou've already chosen the best response.0
\(\ \Huge \left \frac{1}{x}  \frac{1}{2} \right < 0.2 \)
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
what are you trying to solve?
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
i think you must start with \[\frac{2x}{2x}<0.2\]
 one year ago

Study23Best ResponseYou've already chosen the best response.0
It's in the format of \(\ \Huge \left f(x)  L \right < \epsilon \). Im trying to factor that expression so I can use the end result to find \(\ \delta \).
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
\[0.2<\frac{2x}{2x}<0.2\] is the next step
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
you probably are taking the limit as \(x\to 2\) so you have control over the size of the numerator
 one year ago

Study23Best ResponseYou've already chosen the best response.0
Yes, I am taking the lim as x approaches 2
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
or you can write \[\frac{2x}{2x}=\frac{1}{2}\frac{x2}{x}<0.2\] so that \[\frac{x2}{x}<0.4\]
 one year ago

Study23Best ResponseYou've already chosen the best response.0
If I do that, then where would I go from there?
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
you have control over \(x2\) that is you can make it as small as you like as for the \(x\) in the denominator, you can simply say that since you are taking the limit as \(x\to \frac{1}{2}\) you can assert that it is say between \(\frac{1}{3}\) and \(\frac{2}{3}\) so that the whole thing will be largest when the denominator is smallest, namely when it is \(\frac{1}{3}\) giving the inequality \[\frac{2x}{x}<3x2\]
 one year ago

Study23Best ResponseYou've already chosen the best response.0
How would I find \(\ \delta ?\)
 one year ago
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