An even function f(x) of period 2 is given on the interval [0, ] by the formula

An even function f(x) of period 2π is given on the interval [0, π] by the formula y = x/π

(a) Using the even-ness property of the function, draw the graph of the function for –π ≤ x ≤ π.

(b) Using the periodicity property of the function, draw the graph of the function for –4π ≤ x ≤ 4π.

(c) Draw also the graph of the function

The function h(x) = 1/2 + a cos x is used as an approximation to f(x) by choosing the value for the constant a which makes the total squared error, [h(x) – f(x)]², over [0, π] a minimum, that is the value of a which minimizes

and that E

(a) is a minimum when a = –4/π². Draw a graph of the difference, h(x) – f(x), between the approximation and the original function, for 0 ≤ x ≤ π. What is its period?

Transcribed Image Text:

g(x) =//=// = cos x, for -4 x 4.