FunctionHard
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
Create a free account to view solution
View Solution FreeMore Function Questions
If f : R → R f(x) = cos (5x + 2) then the value of f−1(x) is -...If g {f(x)} =| sin x | and f{g(x)} = (sin √x)2, then...If [x2] + x = a has solution(s), a ∈ N, then ′a′ may be (where [.] denotes greatest integer function)-...Let f : R → R be a differentiable function having f(2) = 6, f′(2). Then dt equals...If f(x) = cos x + sin x, [x] denoting the greatest integer function, then -...