If lim x- 2 x^n - 2^n/x - 2 = 80 , find 'n' belonging to natural numbers.

The given limit is, limx2xn-2nx-2=80After putting limit we can see that it is coming to be00 form, so using L'hospital rule we get, limx2ddxxn-2nddxx-2=80limx2nxn-1-01-0=80Now putting the limit we get, n2n-1=80n2n-1=2×2×2×2×5means if we will put n = 5 we will get 5×25-1=80So n = 5.

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