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M1550-Exam4-Sol

# M1550-Exam4-Sol - E trau11550(30 EXAM 4 Instructions You...

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Unformatted text preview: E trau11550(30) 11/23/2010 EXAM 4 Instructions: You must Show your work to receive credit. Scratch paper will not be collected, so you must write all your work that you wish to have graded on the exam. No calculators! There are problems on both sides of the paper! Problem 1 [12 points] Given below is the graph of a function f. Use this graph to ﬁnd: a). j: f(m)d3: = b). j: f(3:]dw = 0). Near under cam-Th: Same a? side q- =>area : 44:16. in). ATM under craft: right ”twat: ,W‘HI base 2, hﬂ‘ 4' = .. 2"} =- 3“ > area - .12.... ‘1'. Problem 2 [8 points] Calculate the sum: assuming that: Zak=l,and 233%: In to 2(30K-b K): aﬁau—ﬁb.‘ =3--\ 3=O “— “W”; Problem 3 [8 points] If 1 3 ﬁx) 5 2, then: .3 [12mm- \0= 10; 262-2). I 48‘: {.ma.x< 02—2) 2: \0-2=20 Probiem 4 [8 points] Assuming that f: f(a;) dx = 10, and that f: f(3:) d3: = 3, ﬁnd /: f(a:)dx=- 5:4(X7AX = .— SHIN Ax = — [ 5300“" SHli w,‘ " “— 1'0 -3] : —? m 3 Problem 5 [12 points] If. then ﬁnd: Problem 6 [12 points] Given that f'(:c) = Bx2 +1 and that f(0) = 3, ﬁnd ﬂx). 3W): Ham v:- (\$K1-l- 0(1):. a ﬂex—ea. ‘ y m 1H0) = Oil—0%: = C }¢>Q=3 5’40} = 3 Problem 7 [16 points] Find: Problem 8 [16 points] Find: a). 1+3? :0. UL = arc’mn (x) = \ du 1+)? ax arctan3 (:c) dz 10). / cos(x)esm(‘”)dx Problem 9 [8 points] Use elementary geometry to ﬁnd: 3 / V9—32 d3: *3 j: J‘?—)(1 £720) %X ’2. 115:“ 3 K413 5‘? Radetxr. HA: grate '. 911' Area. under khe ‘34-‘11.“ ts Mtg-a. cam‘e' 1::‘1 WAX =' f(x) = /1 ﬂ ln(t2)dt Bonus [10 points] If ﬁnd f’(:c). A (>0 = SUM?) A1- 85 Fire 3:: Am due), “-T—(x) = A0170 1'00 = mm (W =: 2..__|__=_/ij Jam?) 26? “£30 ...
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