InterviewSolution
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InterviewSolution
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Let m and n be two positive integers greater than 1.If `lim_(alpha->0) (e^(cos alpha^n)-e)/(alpha^m)=-(e/2)` then the value of `m/n` is |
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Answer» `lim_(alpha->0)(e(e^(cosalpha^n)-1))/(alpha^m)` `=lim_(alpha->0)(e(cosalpha^n-1)/alpha^m)` `=-elim_(alpha->0)(1-cosalpha^n)/alpha^m` `=-2elim_(alpha->0)(sin(alpha^n)/2*sin(alpha^n)/2)/(alpha^n/2*alpha^m*alpha^n/2)` `=2e*alpha^(2n)/(4alpha^m` `alpha^(2n-m)=1` `2n-m=0` `m/n=2`. |
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