TRUE/FALSE:Statement 1: The function `f(x)=x^2+tan^(-1)x` is a non-periodic function. Statement 2: The sum of two non-periodic functions is always non-periodic.

Each question has four choices, a,b,c and d,out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. if both the statements are true and statement 2 is the correct explanation of statement 1. If both the statements are true but statement 2 is not the correct explanation of statement 1. If statement is True and statement2 is false. If statement1 is false and statement2 is true. Consider the function f(x)=sin(k x)+{x}, where (x) represents the fractional part function. Statement 1 : f(x) is periodic for k=mpi, where m is a rational number Statement 2 : The sum of two periodic functions is always periodic.

Prove that function f(x)=cos sqrt(x) is non-periodic.

Integrate the functions (e^(tan^(-1)x))/(1+x^(2))

The function f(x)=sin(log(x+sqrt(1+x^2))) is (a) even function (b) odd function (c) neither even nor odd (d) periodic function

Which of the following is not a periodic function with period 2pi ?

The period of the function y= sin 2x is

Statement 1: If f(x) is an odd function, then f^(prime)(x) is an even function. Statement 2: If f^(prime)(x) is an even function, then f(x) is an odd function.

If f(x)=sinx+cosa x is a periodic function, show that a is a rational number

Statement 1 : For a continuous surjective function f: RvecR ,f(x) can never be a periodic function. Statement 2: For a surjective function f: RvecR ,f(x) to be periodic, it should necessarily be a discontinuous function.