InterviewSolution
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InterviewSolution
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If `Lim_(xto oo) "sin"((pi(1-cos^(m)x))/(x^(n)))` exists and non-zero where `m,n in N` thenA. m=1 , n=1B. m=1 , n=2C. m=2 , n=2D. m=3 , n=2 |
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Answer» Correct Answer - A When m=1, n=1 `underset(nto oo)Lim"sin"((pi(1-cosx))/(x))=sin0=0` When m=1 , n=2 `underset(nto oo)Lim"sin"((pi(1-cosx))/(x^(2)))=sin(pi//2)=1` When m=n=2 `underset(nto oo)Lim"sin"((pi(1-cos^(2)x))/(x^(2)))=underset(nto oo)Lim"sin"((pi(1-cosx)(1+cosx))/(x^(2)))=sin(pi)=0` When m=3 , n=2 `underset(nto oo)Lim"sin"((pi(1-cos^(3)x))/(x^(2)))=underset(nto oo)Lim"sin"((pi(1-cosx)(1+cos^(2)x+cosx))/(x^(2)))=sin((3pi)/(2))=-1` |
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