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fall09 solutions

# fall09 solutions - F6q N ITH 1 40T est I I t f r l ogz(r 1...

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NITH 140 Test I - 1. (2 pts.) (rnultiple-choice question) It f (r) following statements are tnre? \ '6= fi{x+) \ t=z/r \ : D --> A) Fahe Select the correct arrsw€]r. A) There is a number c in the interval (1,3) suchthat /(c) : tl. B) There is a number r: in the interval (1.3) such that ry(r:) : g. C) Thereis a nuntber r: in the interval (1,3) such that .f (c): g(r:). D) None of the above are tnre. :) 4trn 1o / h f gl + fhet€ ; 4 r c | = O t c € ( t ) , ( h n l d * t ' V q f u e Write the (capital) letter of the answer in this box 2. (a pts.) Consicler the function F 6 q : logz(r * 1) and g(.r) : 3/:r. then which of the b) vh< c) Let Are there numbers for n, and b suchthat lirrr.,*r.f (t) exists'/ of the limit. .Iustify your answer. at >to ftr^) c /wac h fu* ' [q) i f : r ( 1 r > 1 . If so, find the values of a and Ir and the value ,,,, : { ,t:2 - rt . r - 1 3 i f : r * b i f &'wt- & D^/E xt l- /--t ftrt = 4i r--u ?(+ LF la qr* 4',n^- (x'-q)*o ](+ 1' /") va. xs 4- \$rxl = ,ha\ra /A"'r'ry {r c. rt u,-t- ( lt+ L) x" L- & = .h-,-t- (x+t) x - , x r L = b + L J,*.,. ( rn = an'',-- {tx) :=) x - + 1 + ' ' x + t - /11//,4 (; \$tn : z Z=A+t -1 6l-t) Answer: Option 1: The limit does not exist for any values of a,and b. Check this borl .h rn = frr) -2 B) con.{.

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