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Find the periods of following functions....

Find the periods of following functions.
`{:((i)f(x)=[sin3x]+abs(cos6x),(ii)f(x)=1/2{abs(sinx)/cosx+abs(cosx)/sinx}),((iii)f(x)=e^(cos^(4)pix+x-[x]+cos^(2)pix),(iv)f(x)=3sin""(pix)/3+4cos""(pix)/4):}`
`{:((v)f(x)=cos3x+sinsqrt(3)pix,(vi)f(x)=sin""(pix)/(n!)-cos(pix)/((n+1)!)),((vii)f(x)=x-[x-b],(viii)f(x)=e^(In(sinx))+tan^(3)x-cosec(3x-5)):}`

Text Solution

Verified by Experts

The correct Answer is:
(i) `2/3pi` (ii) `2pi` (iii) 1 (iv) 24 (v) Does not exist (vi) 2(n+1)! (vii) 1 (viii) `2pi`
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Find the period of the following function (i) f(x) =|sinx|+|cosx| (ii) f(x)=cos(cosx)+cos(sinx) (iii) f(x)= (|sinx+cosx|)/(|sinx|+|cosx|)

Knowledge Check

  • The period of f(x)=sin""(2pix)/(3)+ cos""(pix)/(2) , is

    A
    3
    B
    4
    C
    6
    D
    12

  • The period of the function f(x)=|sin 3x|+| cos 3x| , is

    A
    `(pi)/(2)`
    B
    `(pi)/(6)`
    C
    `(3pi)/(2)`
    D
    `pi`

  • The period of the fuction f(x)=sin""((pix)/(n!))+ cos((pix)/((n+1)!)) , is

    A
    `2xx(n+1)!`
    B
    `2(n!)`
    C
    `n+1`
    D
    none of these

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