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Find the value of alpha so that ("lim")(...

Find the value of `alpha` so that `("lim")_(xvec0)1/(x^2)(e^(alphax)-e^x-x)=3/2`

Text Solution

Verified by Experts

`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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