Over what intervals are the following functions continuous? - Please see attached file for full problem description.
Over what intervals are the following functions continuous? Justify your answer using the definition of continuity.
a.
b.
Let f and ...
Continuous Functions - Suppose that f(x) satisfies the functional equation
f(x + y) = f(x) + f(y)
for all x,y in R (the real numbers). Prove that if f(x) is continuous that f(x) = cx where c is a constant. What ...
Fourier Series of a Periodic Fuction : Convergence - Work out the Fourier series of f, given over one period as follows.
At which values of x does the series fail to converge to f(x)? To what values does it converge at those points?
(h) |cos x| for ...