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Draw the graph of y=1/(log(e)x)...

Draw the graph of `y=1/(log_(e)x)`

Text Solution

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`y=xe^(-x)`
Let `(dy)/(dx)=0`
`rArr e^(-x)-xe^(-x)=0 rArr x=1`
Also at `x=1, (dy)/(dx)` changes sign from `+ve` to `-ve`, hence `x=1` is the point of maxima.
When `x to -infty, y to -infty`
Also `lim_(x to infty)xe^(-x) =lim_( xto infty)x/e^(x)=lim_(x to infty)1/e^(x)=0, f(0)=0`

Range of the function is `(-infty, f(1))` or `(-finfty, e^(-1))`
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