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Find the period of (i) `f(x)=sin pi x +{x//3}`, where {.} represents the fractional part. (ii) `f(x)=|sin 7x|-"cos"^(4)(3x)/(4)+"tan"(2x)/(3)` |
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Answer» (i) `f(x)=sin pi x +{x//3}`, where {.} represents the fractional part Period of ` sin pi x " is " (2pi)/(pi)=2` Period of `{x//3} " is " (1)/(1//3)=3` Therefore, period of f(x) is L.C.M. of `(2,3)=6` (ii) `f(x)=|sin 7x|-"cos"^(4)(3x)/(4)+"tan"(2x)/(3)` Period of `|sin 7x| " is " (pi)/(7)` Period of `"cos"^(4)(3x)/(4) " is " (pi)/(3//4)=(4pi)/(3)` Period of `tan(2x)/(3) " is " (pi)/(2//3)=(3pi)/(2)` Therefore, period of f(x) is L.C.M. of `((pi)/(7),(4pi)/(3),(3pi)/(2))=pi xx (L.C.M. of (1,4,3))/(H.C.F. of (7,3,2)` `=12 pi` |
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