A particular periodic function has Fourier Series FS(x) given by FS(x) = 20 + b, sin where the coefficients b₁ are given by bn n=1 ппх " 2 1 試 4 ппх (9x+2) sin dx. 2 (a) What is the period of the function? (b) Without doing any integration, write down the average value of FS(x) over one period. (c) Find an expression for br (in terms of n).

Find the Fourier Cosine Transform of the function f(x) = ae^(-bx) if x > 0     if a = 15.1 and b = 4 . Then, evaluate the transform if w = 15.

1+ sec(t) 1+ cos(t) Simplify to a single trig function.

Use the results to prove the fourier series f(x) (picture)

A cable hangs between two poles of equal height and 26 feet apart. Set up a coordinate system where the poles are 13, where x is measured in feet. The height (in feet) of the cable at position x is placed at x = -13 and x = h(x) = 18 cosh(x/18), where cosh(x) = (eª + e¯*)/2 is the hyperbolic cosine, which is an important function in physics and engineering. The cable is feet long.

need help with sine function for fourier series

Q3/ Find Fourier cosine transform of the function f (x) = 2x ,0 < x < 4

The trigonometric substitution x - 2 = 3 sec 0 could be useful in integrating a function (i.e., an integrand) involving... (a) √x² 4x + 5 (b) x² 4x - 5 (c) 9 - (x - 2)² (a) √ (x - 2)² +9 (e) 4x9

C- Find f' of the following: 1) √2x³ - 2² + ln x² 2) 3x³x+1 3) sin-¹(³).

An ODE p(D)y = f(x) has a solution y=(x^2*sinx) + (x*cosx). Determine the roots of p(D). a. +-i, +-i, +-1 b. +-i, +-i c. 1, +-i, -1 d. 1, +-i