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Unformatted text preview: f ( x ) = √x if x < 3x if 0 ≤ x < 3 ( x3) 2 if x > 3 Evaluate each limit, if it exists. (a) lim x → + f ( x ) (b) lim x →f ( x ) (c) lim x → 3 + f ( x ) (d) lim x → 3f ( x ) (e) Where is f discontinuous? 5 Scratch 6 3. Find the limit. (a) lim x →3 1 ( x + 3) 4 (b) lim x →∞ 3 x 21 2 x 2 + 7 7 Scratch 8 4. Prove that lim x → x 2 cos(1 /x 2 ) = 0 9 Scratch 10 5. Find an interval of length 1 that contains a solution to x 4 + x3 = 0 11 Scratch 12 6. Using the precise deﬁnition of a limit, prove that lim x → 2 (145 x ) = 4 13...
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This note was uploaded on 04/09/2011 for the course MATH 3a taught by Professor Shu during the Winter '08 term at UCSB.
 Winter '08
 Shu
 Math

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