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geerky42
 one year ago
I need a quick favor:
I want strictly increasing elementary function \(f(x)\) such that \(f(0)=0\), \(f\left(\frac12\right)=1\), and \(\displaystyle \lim_{x\to1^}f(x) = \infty\).
I just want one example of function that satisfies given conditions. Cannot figure this out...
geerky42
 one year ago
I need a quick favor: I want strictly increasing elementary function \(f(x)\) such that \(f(0)=0\), \(f\left(\frac12\right)=1\), and \(\displaystyle \lim_{x\to1^}f(x) = \infty\). I just want one example of function that satisfies given conditions. Cannot figure this out...

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Loser66
 one year ago
Best ResponseYou've already chosen the best response.0How about this \(f(x) =\dfrac{xx^2}{1x}\) f(0) =0 \(f(1/2) =\dfrac{1/21/4}{11/2}=1\) as x approach 1 from the left , lim > infinitive Does it work?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0and if we simplify, we get f(x) =x, it is increasing, right?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1You think this works? $$ f(x)=\frac{x(x+\frac{3}{2})}{x1}\\ $$

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1http://www.wolframalpha.com/input/?i=x%28x%2B3%2F2%29%2F%28x1%29

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0@ybarrap but your graph is decreasing from x =1

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1Or maybe... $$ f(x)=\frac{x(x+\frac{3}{2})}{1x}\\ $$ http://www.wolframalpha.com/input/?i=x%28x%2B3%2F2%29%2F%281x%29

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0@ybarrap Not exactly what I needed, but I modified it to \(f(x) = \dfrac{x(x+\frac32)}{2(x1)}\), which works for me. Thanks!

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0@Loser66 Well, I want \(\lim_{x\to1^}f(x)\) to be \(\infty\),

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0But I got what I needed, thanks!
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