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Worksheet1 - Math 17A Kouba Worksheet 1 1 Use the...

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Unformatted text preview: Math 17A Kouba Worksheet 1 1.) Use the three-step definition of continuity for each of the following problems. 2 ~ _ a.) Let f(x) = {:10 +23 ’ 1:: : _1 Determine if f is continuous at a: = —1. (E + 1 , if a: Z 0 2 _ x2 , if :10 < 0' Determine if g is continuous at a: = 0. b.) Let g(m) = { ac — 2 , if a: > 1 e.) Let f(m) = { 0 , if m = 1 Determine if f is continuous at a: = 1. —:c , ifzv < 1. 2.) Use approved shortcuts and facts from class to determine (with a brief explanation) the {Ix—values for which each of the following functions is continuous. 3-) “33) =$5+w4+m3+x2+$+1 b.) 9(110) = 3:321:34 3 c.) f(:c) = :21; 4 d.) m) 2 CW3 _ x) 3.) Determine constants A and B so that each of the following functions is continuous for all values of :17. Start by drawing a“fake” graph. Then use limits. 2_ {w , M716 x—6 A , ifzc=6. AZm—A , ifol 2 , ifm<1. , ifx<0 3 , ifoO 5 , if$>2 AID—B , ifo—l 2x+3A+B , if~1<x§1 { 1 + 3 , ifxgl d.)f(a:)={A:c2+B , if1<$£2 { 4 , if$>1 ...
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