Exam 1 Solution CHE 2120 Fall 2004

# Exam 1 Solution CHE 2120 Fall 2004 - ChE 2120 Exam 1(l(35...

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Unformatted text preview: ChE 2120 Exam 1 September 17, 2004 (l) (35 pts) Consider the following equation: 36 =2x Use a numerical method of your choice to solve for x. Perform 3 iterations of this method and show all your work. Hint: there is one root in the interval -0.75 < x < 0.75. 3C) (2) Consider the function f(x) shown below, to solve f(x) = 0 for x. a. (10 pts) Sketch two iterations of the false position method. Use x; = -l and x” = 2. IO 1 . 0.8 I 0.6 0.4 0.2 ﬁx) b. (i0 pts) Sketch two iterations of the secant method. Use x. 1 = -1 and In I 2. l 0 1M ﬂ-B w ' . f0!) -1 -05 U 0.5 1.5 2 i D " c. (10 pts) Describe the similarities and difference between these two methods (use the back of the page if necessary). Boli- mthgdls (omega? \$1 (Mitt: smug: mi” a Erin-w: Qme- EDH‘ “AM Mr “00+ N" H": is be the 00!..fo where; 'Jrlw C‘Io‘bbﬁ K'CWS‘B. The dig-QQJLEWQ @ 1'5 \‘WW thew I P '\——-J cfeclclle X to Kept-ice W/ Xr for @5666 74% N21”: Kmart-10%, I (Uo"~.t.l:.lm._t~o{‘x bag}; -——9) F51?“ R’s'HMﬂJo/és {v fee/D SEW CIILg‘MﬁQ: 7L); 1%, .ggawt’W ’uICH n6+.Jr’VUlj€)wéuf my Casz :2. Men 5}» Secm+ Jf'VwaeAf in I4— Mgg HM; M93; MCW+ 63 #11an To make'rB NHL SQCMWLM' . MY T% £0er “have Probfems bf Hm 5(0ﬁe Ma ﬂoat is app/mt 26m 9’? aﬁth 322%: due. f0 mama/ma mars (th am affrox.%f3?b), Eu} 7%»: (SSW .95; 5% in %Z"é)(a)¢p(a. (3) a. (20 pts) Apply Gauss elimination to solve A x = b for x. O 2 : Li {(0 -IO = '10 {a "‘8 2 *Co *(9 [2 = 3 Al H1 -2o = -20 (D ‘8 =-I7 X3. 1 2 25' (3) b. (15 pts) Characterize the solution for x as one of the following: One unique solution exists. t/ No solution exists. _ An inﬁnite number of solutions exist. 7 Explain your answer. This x'neﬁm/i'ﬁf) 06cm. bec'me Hue lasl a Fews 6% Whit am (axon/Ali W Same?) l(heir (ck {ﬁftiedinj o E exacllj SW gof TM c1 lineS [am] He? MW) +0 km 0- 30’“ 77m_ 4,124 c222 P_a3?_§_//e/._ (See await) futility “a” ...
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Exam 1 Solution CHE 2120 Fall 2004 - ChE 2120 Exam 1(l(35...

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