FunctionMedium
Question
Which of the following functions are periodic -
Options
A.sin x + cos x
B.cos x + 
C.cos πx + {2x}
D.in{x} + sin2x ({x} denotes the fractional part of x)
Solution
(A) sin x + cos x = √2 sin 
→ Periodic
(B) cos x → period 2π
→ period π
So period of cos x +
= 2π
(C) cos πx period 2
{2x} → period
so period of cos πx + {2x} = 2
(D) ln {x} → period 1
sin 2x → period π
ln {x} + sin 2x → no period
→ Periodic(B) cos x → period 2π
→ period πSo period of cos x +
= 2π(C) cos πx period 2
{2x} → period
so period of cos πx + {2x} = 2
(D) ln {x} → period 1
sin 2x → period π
ln {x} + sin 2x → no period
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