I need to know which ones are true and which are false. If they are true I need to prove it. If they are false I need a counterexample as to why.
a) If f is uniformly continuous on (0, infinity) and g is positive and bounded on (0, infinity) the fg is uniformly continuous on (0, infinity).
b) The function xlog(1/x) is uniformly continuous on (0,1).
c) The function cos(x)/(mx+b) is uniformly continuous on (0,1) for all nonzero m,b in the Reals.
d) If f,g are uniformly continuous on an interval [a,b] and g(x) does NOT = 0 for x in [a,b], then f/g is uniformly continuous on [a,b]. TRUE (I dont know how to prove though!)
a) If f is uniformly continuous on (0, infinity) and g is positive and bounded on (0, infinity) the fg is uniformly continuous on (0, infinity).
b) The function xlog(1/x) is uniformly continuous on (0,1).
c) The function cos(x)/(mx+b) is uniformly continuous on (0,1) for all nonzero m,b in the Reals.
d) If f,g are uniformly continuous on an interval [a,b] and g(x) does NOT = 0 for x in [a,b], then f/g is uniformly continuous on [a,b]. TRUE (I dont know how to prove though!)