Fourier Series Quiz

$rac{x}{2} - rac{x^3}{3} + rac{x^5}{5} - rac{x^7}{7} + ...$

$rac{x}{2} - rac{x^2}{2} + rac{x^3}{3} - rac{x^4}{4} + ...$

$rac{x}{2} - rac{x^3}{3!} + rac{x^5}{5!} - rac{x^7}{7!} + ...$ (correct)

$rac{x}{2} - rac{x^2}{2!} + rac{x^3}{3!} - rac{x^4}{4!} + ...$

By using only Taylor's theorem

By setting the function to repeat after a specific value of x

By using only Maclaurin's theorem

By defining them to repeat after a certain interval (correct)

$F(x) = \frac{1}{T} \int_{-T/2}^{T/2} f(t)e^{-i2\pi nt/T} dt$

$F(x) = \frac{a_0}{2}$

$F(x) = \frac{1}{\pi} \int_{-\pi}^{\pi} f(t) \left(\frac{\sin((2n+1)t)}{\sin(t)}\right) dt$

$F(x) = a_0 + \sum_{n=1}^\infty (a_n \cos(nx) + b_n \sin(nx))$ (correct)

<p>A function that repeats itself after a specific interval</p> Signup and view all the answers

<p>Trigonometric functions can be used to expand the algebraic function into an infinite series</p> Signup and view all the answers