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t Math 106 A Quiz 02 page 1 01/23/13 Name Suages tek soln. 1a. Suppose that f’(x) = 4/(x? — 2x +3) for some function f. According to “Theorem 3” what is the maximum possible error if LHS(40) is used as an approximation to I f(x) dx? Show all formulas from Theorem 3 used in your answer. 22 here y M. may, tale A pe Fl) [hy] 6 HS IF 6) o [-44] 7 a dik 2 he The 3 gis a ape lanl 4 2° 2-(4- 7" i* 2 Ja 85 os" “2-90 2.9 to 4% Huh oF [= - Lac(s)| < 0.62 (or, epvteloatly , Lus(te) ~ 0.625 < T < Ut/e)10@- 1b. Suppose in fact that LHS(40)=100. Whaf is the smallest that if f(x) dx can be? Th ¢Hs(1)- 0.625 = (O-O.605 = 2a. Suppose that the graph of g’(zx) is as shown below for some function g. According to “Theorem 3” what is the 3 maximum possible error if MID(30) is used as an approximation to / g(x) dx? Show all formulas from Theorem 3 used in your answer. 3 1/0 Se dns Hat the maxim vale 4 |94(0)] 6 be x in (-2, x) 7 hd “ie KOS gifs 2s be eee 35 6 omits) From Ho 38 the mene oss ar 25 20 AS 10 05 0 OF 10 15 20 25 30 35 v=, i+? 6 K, (6-4) (& rup()) 24 (n* Zz = S(Y lo ogesok 3 24 (30) = 2b. Suppose in fact that MID(30)=200. What is the biggest that [ g(x) dx can be? (' c it 0 ) fh LOO +E =[200- og6os.. { 
