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Study23
 2 years 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?
Study23
 2 years 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?

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Study23
 2 years ago
Best ResponseYou've already chosen the best response.0\(\ \Huge \left \frac{1}{x}  \frac{1}{2} \right < 0.2 \)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0what are you trying to solve?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0i think you must start with \[\frac{2x}{2x}<0.2\]

Study23
 2 years ago
Best ResponseYou've already chosen the best response.0It'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 \(\ \delta \).

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0\[0.2<\frac{2x}{2x}<0.2\] is the next step

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0you probably are taking the limit as \(x\to 2\) so you have control over the size of the numerator

Study23
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, I am taking the lim as x approaches 2

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0or you can write \[\frac{2x}{2x}=\frac{1}{2}\frac{x2}{x}<0.2\] so that \[\frac{x2}{x}<0.4\]

Study23
 2 years ago
Best ResponseYou've already chosen the best response.0If I do that, then where would I go from there?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0you 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 \[\frac{2x}{x}<3x2\]

Study23
 2 years ago
Best ResponseYou've already chosen the best response.0How would I find \(\ \delta ?\)
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