Recent content by varignon

Homework Statement Let f be a function which is continuous on a closed interval [a,b] with f(c) > 0 for some c\in[a,b]. Show that there is a closed interval [r,s] with c\in[r,s]\subseteq[a,b] such that f(x) > 0 for all x\in[r,s]. Homework Equations Hint let epsilon = f(c)/2 and find...

\delta has to be sqrt(2), which is still greater than \delta/2. Further investigation revealed that this seemed to be the case for x^3 etc too. I tried it with 1/(x^2), as a=1, l=1, that seemed to work quite nicely. Is this a useful candidate?

If i let b =1, and if m < 1, then \delta gets smaller more quickly than \epsilon. Is f(x) = 0.25x + 1 a suitable answer to this question?

Homework Statement Give an example of a function f for which the following assertion is false: If |f(x)-l|<\epsilon when 0<|x-a|<\delta, then |f(x)-l|<\epsilon/2, when 0<|x-a|<\delta/2 The Attempt at a Solution I am really not quite sure what I am looking for here. I think i want...