Key quiz 2 fall 2010

Key quiz 2 fall 2010 - P LEDGED _____________ Quiz 2, M ath...

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Unformatted text preview: P LEDGED _____________ Quiz 2, M ath 111 You are to work t his quiz at o ne s itting w ithout the use o f notes, text, i nternet, o r a nother person. This quiz is to represent y our work a nd y our u nderstanding o f these concepts. D ue Friday, S eptember 10th. 1. Suppose we wish t o know i f f (x) interval [-4,0]. = v'25 - x 2 achieves a h eight o f 4 for one o r more x values in t he a) ( 2 points) S tate t he I ntermediate Value T heorem. + IF i s eav-rh.nv..cu..$ "'- ,S THEN a.t OV'"' [ a.Jb] + (0-') o..Y"\..d. + Cb) L eastone c be:twt:e-rt rCc):: 5LLt:n 0- o.nd.. b e x I S+.s R b ) (2 points) Clearly e xplain how t he c onditions of t his t heorem a re e ither m et o r n ot m et, i n a n a ttempt t o a pply i t t o t he s ituation described above. :r F " -F (XI :;; .J;;2 5" - X " 0 VIlA [=-s} s J; [-'-I,oJ fC-4) = 3 CL '".2.- 1<. i s ( ! oy)'h'f)UOt.A4 ' f1 4 -FCo] = -5 : rvTk c) ( 2 points) F ind t he x-value g uaranteed t o e xist b y t he t heorem i n t his s ituation, o r e xplain why i t fails t o exist. . " l1tEN ,l X-=- -3 i ntuva-e is ' In 0 ..= '+he., - 4 < -X-=:-3 -< b = 0 2. Suppose f (x) = 1 1 2x (a) ( 2 points) S tate t he definition of t he derivative . f-lX-+--h) - .fI()C") ;;:: I (c) (1 point) F ind t he e quation o f t he t angent line t o f (x) a t x = 1. . f( II = /_ -1"(,)::. J(,) : : _-7- =- -/ ( I) - I ) -:l. ( /- :HI)) =-- , ::: l <5/ af 6 3. ( 2 points each) E valuate t he following limits a nd provide (in words) t he g raphical i nterpretation for each. :: I$"in (-ml -I :0 \ - 'I C;OS{-Tr) = - \ c \ l 4. (4 points) F ind t he values o f a a nd b t hat make t he following f unction c ontinuous everywhere. -+-err x. <./. -.:< I 0.... \ - :;:l<X-") X2 f (x) n = { + 2a 6 3ax + b 3 x + 2bx(ln x - 1) X> 1 if x < - 2 if 2x if 1 < x 1 ___ )C =-loo...4-b = ---- '0 (30-.)<+'0) :::: ')( 1- )C--) -+- X> o f(. ,+ J b ('3')( -=- r; ...
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This note was uploaded on 12/05/2011 for the course MATH 111 taught by Professor Bang during the Fall '08 term at Emory.

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Key quiz 2 fall 2010 - P LEDGED _____________ Quiz 2, M ath...

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