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Question

Let m and n be two positive integers greater than 1. If
limα0(ecos(αn)eαm)=(e2)The value of mn is

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Solution

elimα0(ecosαn11cosαn1cosαn1αm)=e2
limα0(1cosαnαm)=12
limα0(1cosαn(αn)2)α2nm=12
2nm=0
mn=2

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