practice2 - f at a point x ∈ dom ( f ). (b) Show that if...

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MATH 131A section 2: Practice Midterm 2. Please write clearly, and show your reasoning with mathematical rigor. You may use any correct rule about the algebra or order structure of R from Section 3 without proving it. Name: Student ID: 1. Suppose ( s n ) is a given sequence in IR , and suppose limsup( s n ) 2 1 . Show that there is a convergent subsequence. 2. Suppose b n > 0 ,n = 1 , 2 , 3 ,... and b n 1 n 2 for n 100. Show that Σ b n converges. 3. (a) State the definition of continuity for a function
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Unformatted text preview: 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. (a) State the definition of differentiability for a function f at a point x ∈ dom ( f ). (b) Show that f ( x ) = | x | is not differentiable at x = 0. 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.

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