11METHOD 1 : Use the expansions of cos x and ex and get ur answer
METHOD 2 : collect ex and cos x in the numerator and apply 1-cos x=2sin2x/2 and get ur answer
METHOD 3 : Apply L hospital rule as per ur convenience
Find integer n for which \lim\frac{cos^2{x}-cosx-e^{x}cosx+e^{x}-x/2}{x^{n}} is a finite non zero number
x→0
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UP 0 DOWN 0 1 6
6 Answers
11
11Eventually this is what it boils down to
1+exn.xn-2-12nxn-1
But I think expansion is a much better way out here...
1use cos2x=(x-x2/2)2
=x2(1-x/2)2=x2-x3 (applying bino.)
cosx=x-x2/2
e^x=1+x+x2/2
where ever necessary apply bino., and this way ull be able to solve this one.
for other triers...i think ive seen this problem before and the answer is either 4, or 3 i dont remember..(possibility that it mite have been a diff. problem)
cheers!!
11Great, gordo, that cosx substitution seems to be a rare one - rarer than the usual cosx≈1....thanx, I'm learning more from ur posts...
1We can also differentiate numerator repeatedly and keep putting x=0, it will become non-zero in nth derivative
here you can do this but if the expressions become complex it will consume a lot of time and hence should be avoided
1soumik, sorry dude, (nice way to show ones mistake),
i was in real hurry when i typed it,
cosx=1-x2/2
by mistake i typed an x in that place.
sorry again to everybody.