Fourier series -1

The incorrect statement from the following choices is

• The product of two even functions is an even function

• The product of two odd functions is an even function

• The product of an odd function and an even function is an even function

• The product of an odd function and an even function is an odd function

The incorrect statement from the following choices is

• sinx is an odd function

• sin2x is an odd function

• sinx² is an odd function

• sinx² is an even function

An example of an odd function is

• x³

• x²

• xsinx

• sinx+cosx

sinx+cosx is

• an odd function

• an even function

• neither an odd function nor an even function

• both odd and even function

For any integer n the value of cosnπ is

• 1

• 0

• -1

• (-1)ⁿ

If f(x) is an even function then for all values of n the value of b_n is

• 1

• -1

• n

• 0

The Fourier coefficient a_o for f(x) = e^x in (-π,π ) is

• sinhπ/π

• e^π+e^-π

• e^π-e^-π

• 2sinhπ/π

The Fourier coefficient a₀ for f(x) = x sinx in (-π,π) is

• 2π

• 2

• π

• -π

For any integer n the value of sinnπ is

• (-1)ⁿ

• 1

• -1

• 0

The Fourier coefficient a₀ for f(x) = e^x in (0,2π) is

• e^2π-1/π

• e^2π-1/2π

• e^2π-1

• 0