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Find the value of a so that lim(xto0) (e...

Find the value of a so that `lim_(xto0) (e^(ax)-e^(x)-x)=3/2.`

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`underset(xto0)lim(e^(ax)-e^(x)-x)" "`(0/0 form)
`=underset(xto0)lim(ae^(ax)-e^(x)-1)/(2x)" "`(Using L'Hospital's Rule)
Since `Drto0" for "xto0,`
So, `Nrto0" for "xto0`
or `ae^(0)-e^(0)-1=0`
or `a=2`
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