Name Math 1A Quiz 2 September 9 2008 GSI Rob Bayer You have until 4 30 to complete this quiz You must show your work 1 3 pts The graph of a function f x is pictured below Find each of the following or state that they do not exist a lim f x 0 c lim f x DNE e lim f x 1 b d lim f x 1 f lim f x 0 x 0 lim f x 1 x 2 x 1 x 2 x 1 x 1 2 3 pts Prove using the definition of a limit that limx 3 2x 1 7 Let 0 be given We want to find 0 such that 0 x 3 2x 1 7 So we want 2x 6 which is the same as 2 x 3 which happens if x 3 2 Claim 2 works Proof x 3 2 2 x 3 2x 6 3 4 pts Prove using the definition of a limit that lim x 4 Let 0 be given We want to find 0 st 0 x 16 x 4 x 16 x 4 x 4 x 4 x 4 x 16 x 4 Note also that if x 16 1 then 15 x 17 so 15 4 x 4 17 4 Since the x 4 is in the denominator we ll replace it by the smaller thing x 16 x 16 x 4 15 4 We want this to be so we ll guess min 1 15 4 Claim This works Proof If x 16 min 1 15 4 then x 16 1 and x 16 15 4 Be previous work we know x 4 15 4 under these conditions so we can do the following x 4 x 4 x 4 x 4 x 16 x 4 x 16 15 4 15 4 15 4 as was to be shown
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