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experimentXBest ResponseYou've already chosen the best response.0
it is given to prove that x/(1+x) < ln(1+x) < x in the interval [1,1+t] t>0
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
dw:1350718620013:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
dw:1350718731005:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
dw:1350718795042:dw
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
But then, you still haven't considered lnx...
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
why do you need to prove ... ln(2) > 1/2 ?
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
It's not prove.. but.. we have to consider lnx..
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
By considering ln x in [1; 1 + t] (t > 0), ln x in [1; 1 + t] (t > 0), minimum bound : ln(x) = 1 => x = e
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
x/(1+x) < ln(1+x) < x ... perhaps we can use the same argument as we used above.
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
\[ (x+1)^2 > 1+x > 1 \text{ for all x > 0} \\ {1 \over (1+x)^2} < {1 \over 1 +x} < 1 \text{ for all x > 0} \\ \int_0^x {1 \over (1+x)^2} \;dx < \int_0^x {1 \over 1 +x}\;dx < \int_0^x1 \; dx \\ {x \over 1+x} < \ln(1+x) < x \]
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
\[ \ln (x) \text{ in } [1, 1+t], t>0 \] perhaps this would mean show that \( \ln(1)<{t \over 1 +t} < \ln(1+t)\)
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
MVT http://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Mvt2.svg/300pxMvt2.svg.png
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
dw:1350722628100:dw
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dw:1350722670829:dw
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dw:1350722732492:dw
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dw:1350722797470:dw
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experimentXBest ResponseYou've already chosen the best response.0
dw:1350722973766:dwdw:1350723003576:dw
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experimentXBest ResponseYou've already chosen the best response.0
dw:1350723085914:dw
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
f(b)  f(a) / (ba) ?
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
dw:1350724369177:dw
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
OMG! My super smart brother!!
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
lol ... not that smart. Just copied half from your prev answer.
 one year ago
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