Question: 4. Consider the function f : [0, 1] R which is defined by f(x) = 0, 0 x 1/2 , f(x) = 1 - 2x,

4. Consider the function f : [0, 1] R which is defined by

f(x) = 0, 0 x 1/2 ,

f(x) = 1 - 2x, 1/2 x 1

(a) Find the Fourier Sine Series of f(x).

(b) Graph this Fourier Sine Series for 3 x 3. Then determine for what values of x is the (pointwise) limit of the Fourier Sine Series equal to f(x).

(c) Does this Fourier Sine Series converge uniformly to f(x) on [0, 1]? Why?

(d) Does this Fourier Sine Series converge in the mean square sense to f(x) on (0, 1)? Why?

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