InterviewSolution
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InterviewSolution
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Find the period of`f(x)=sinx+tanx/2+sinx/(2^2)+t a n x/(2^3)++sinx/(2^(n-1))+tanx/(2^n)`A. `2pi `B. `2^(n-1)pi `C. `2^(n)pi`D. `n pi ` |
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Answer» Correct Answer - C We have, `f(x)=sum_(r=1)^(n)(sin""(x)/(2^(r-1))+tan""(x)/(2^(r)))` `implies f(x)=sum_(r=1)^(n)f_(r)(x), where" " f_(r)(x)= sin""(x)/(2^(r-1))+tan""(x)/(2^(r))` since each of ` sin""(x)/(2^(r-1)) and (x)/(2^(r ))` are periodic functions with period `2^(r)pi`. Therefore, `f_(r)(x)` is periodic with period ` 2^(r) pi`. But , `f(x)=sum_(r=1)^(n)f_(r)(x)` . Therefore, , f(x) is periodic with period T given by T=LCM of `(2pi, 2^(2)pi, ....,2^(n)pi)=2^(n)pi` |
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