Unformatted text preview: C . (b) Show that g is continuous at every point not in C . Problem 3. (a) State the Generalized Mean Value Theorem. (b) Let f : R → R be a diﬀerentiable function and suppose that f is bounded. Show that f is uniformly continuous. Problem 4. (a) State the deﬁnition for a function f : A → R to be diﬀerentiable on an interval A . (b) Let f : [-1 , 1] → R be the function deﬁned by f ( x ) = ( x 2 sin 1 x 2 x 6 = 0 x = 0 . Show that f is diﬀerentiable, but that its derivative is unbounded. 1...
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- Spring '08
- Math, Continuous function, Metric space, 50 Minutes, Cantor, generalized mean value