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Let f(x)=sin(x/(n!))+cos((2x)/((n+1)!))....

Let `f(x)=sin(x/(n!))+cos((2x)/((n+1)!))`. Find the period of `f(x)`.

Text Solution

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Period of `sin(x/n_1)=T_1`
`T_1/(n!) =2pi`
`T_1=n!(2pi)`
Period of `cos((2x)/(n+1)!)=T_2`
`(2T_2)/((n+1)!)=2pi`
`T_2=(n+1)!pi`
Period of`sin(x/n_1)+cos((2x)/((n+1)!))` is
T such that`n_1T_1=n_2T_2=T`
...
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