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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: find range of xln(x)
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[Post New]5 Dec 2007 20:41:54 IST
    Subject: find range of xln(x)
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umang (229)

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ln(x) means logx to the base e
Umang
    
[Post New]5 Dec 2007 23:23:06 IST
    Subject: Re:find range of xln(x)
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abhujabal (192)

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f(x)=xlnx
f'(x)=1+ lnx =0 for min or max
at lnx= -1, x=1/e, f(x) is min as f''(x)=e>0
f(x)= -1/e at x=1/e
f(x) _> at x_>
 Hence the range is ( -1/e,  )
I hope I am correct.......cheers....
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[Post New]8 Dec 2007 20:52:21 IST
    Subject: find range of xln(x)
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venkat_tatolu (228)

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x must be positive.but the range of logx is R (set of real numbers).
So range is R.

The above method said by abhujabal is mainly used for to find local

maxima or minima.
***T.Venkat***
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[Post New]8 Dec 2007 23:22:21 IST
    Subject: find range of xln(x)
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spideyunlimited (3916)

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abhujabal is correct.
venkat is wrong.
range is [-1/e , infinity)
method given by ahuja is correct.
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