Unformatted text preview: n ∞ a n = 0. (b) Show that Σ n n 2 +1 diverges. 3. (a) State the deﬁnition of continuity for a function f at a point x ∈ dom ( f ). (b) Show that if f is continuous at (0 , 1) and if lim x → + f ( x ) exists, then there exists a continuous extension ˜ f of f on [0 , 1) . 4. Give an example of function f : [0 , 1] → [0 , 1] which is discontinuous at every rational points in [0 , 1]. Explain why. 1...
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This note was uploaded on 11/15/2010 for the course MATH math 131 taught by Professor Kim during the Spring '10 term at UCLA.
 Spring '10
 Kim
 Math, Algebra

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