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The integer n for which `lim_(xto0) ((cosx-1)(cosx-e^(x)))/(x^(n))` is a finite nonzero number is__________.

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The integer n for which `lim_(xto0) ((cosx-1)(cosx-e^(x)))/(x^(n))` is a finite nonzero number is__________.
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Correct Answer - `(3)`
`L= underset(xto0)lim((cosx-1)(cosx-e^(x)))/((1+cosx)x^(n))`
`=underset(xto0)lim(((sinx)/(x))^(2)((1-cosx)/(x)+(e^(x)-1)/(x)))/(x^(n-3))(1)/(1+cosx)`
If L is finite nonzero, then `n=3` (as for `n=1,2,L=0,` and for `n=4,L=oo`.)
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