Test: Fourier Series - Mathematics MCQ

For the function e-x, the linear approximation around x = 2 is

Which of the following functions would have only odd powers of x in its Taylor series expansion about the point x = 0? 

In the Taylor series expansion of exp(x) + sin(x) about the point x = π, the coefficient of (x – π)² is 

The Taylor series expansion of  is given by 

The function x(t) is shown in the figure. Even and odd parts of a unit-step function u(t) are respectively, 

For x = π/6, the sum of series  (cos x)²ⁿ  = cos²x + cos⁴x + ......is 

In the Taylor series expansion of e^x about x = 2, the coefficient of (x-2)⁴ is

The Fourier series expansion of a symmetric and even function, f(x) where 

And  
Will be

The summation of series   is

The Fourier series expansion  of the periodic signal shown below will contain the following nonzero terms 
 

Fourier series for the waveform, f(t) shown in fig. is

The Fourier series for the function f(x)=sin²x is

X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) / T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equation  

The Fourier Series coefficients, of a periodic signal x(t), expressed as 

are given by 
Witch of the following is true? 

f(x), shown in the figure is represented by f(x) =  + b_n sin(nx)}. The value of a₀ is

 

Given the discrete-time sequence x[b] = [2,0,-1,-3,4,1,-1], x(e^jπ) is

The infinite series f(x)  converges to