1.

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

Answer» 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`
Such at `n_1n_2` are to each
`(n!)2pi*n_1=n_2(n+1)!pi`
`2n_1=(n+1)n_2`
`n_1/n_2=(n+1)/2`
when n is own,`n_1/n_2=(n+1)/2`
`n_1=n+1,n_2=2`
`T=2(n+1)!pi`
When n is odd
`n_1/n_2=(n+1)/2`
`n_1=(n+1)/2,n_2=1`
`T=(n+1)!pi=(n+1)!pi`
`T=2(n+1)!pi` when n is even.
`T=(n+1)!pi`, when n is odd.


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