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# Exam 3 - I I,‘-’ M t Li 1 Math 151 Calculus Emmi...

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Unformatted text preview: I I.,‘-’ _ M t Li ' 1 _ Math 151] Calculus Emmi! Surﬁng 1606" Shaw your work! Nam: . i I ' " 1%}. First state the “form” ut‘each limit and then evaluﬂﬁﬁach1tmiL s . -- I #41 sitt(2tn:r} ‘ ' ' ' 4/ J . g'J s.,..d - gusts 't.‘ t l 5h. Iim ———s”‘ {1"} Jr—I-l coshtx] +1 W ” ' .r’ IL . m 5: L Lr-If 19* . . . . .4 . . . la. A farmer has 4 mtiss DI Fencmg mama} to construct twn canals along a river as Show 111 th: diagram. Titers is no: fence 0n the sides ﬁfths fields must in the river. What is the largest Feasible value ﬂfﬂ'lﬂ tats] ﬁrsts):2 + xv in s uart: miles? Justit‘ our answer --- _ r5| .‘t’ Ir“ _ {ﬂied-E . ! -__ I. 'I _ If, - . _" ﬁ‘ X X - _ '- x >r _ H— . _ '3 2 i r / ” _ / _ R 1 i -. ll Lit — L}! ‘t " 3‘ I .r' I. '. d 1- r IE.- F — Pf“: "" .a-d' J 1H,- { f x I gr- ~ ~. / ,1] .5”— 2'? :‘a man walks at 5 ftx'eee and awims at 4 f‘Lr'see. He wants to get to a buoy heated 43 feet From the beach and 3!? feet horizontally ﬁ'em hi5 present pesitien. Use the “Cleaee‘ interval Method” to ﬁnd the value ef x at which the man sheulti enter the water to minimize his travel time ﬁx) te__ the buoy. The domain of The) wii be US): 531}. time: dir H'ln‘i: .5th Tim} T i105 ﬁg ant-[mt FDIHT‘S in the cicmfrﬂ. F_ arm:- f‘\ N ' ' Gram: t- I. . . i- _ at I. _ U511 HE» _. I , . r - .21 ,- . -. .. __ _—- - , -— r — -- -o- . ‘J I - I .- - - 1‘- Wulke x ._ ' :- ' - i? use!) 3 .-/ I i '2' F ' ' - ' I' III a Hat. tin}. f“ I #- ."_ —— —'__'_'—__l——H\. -" an. IF. _ .-r' I _ J I __ ' .t :3 .: .- .”“\ rm. 4. Suppeae that f’(t) = —r-. —1— i and J{(1 I 2} = 1 _ Use antiderivativea to ﬁnd the fnnetmri ﬁt) . Hint: Write an — a: 2 dawn the derivative nfareain ﬁg}; f -——-——_\ 5a“ f 113:3 a 5. agFill in both box es to complete the deﬁnition of the Deﬁtute integral: Jf{x)dx = i '- J H l'. 'il-Z'; I I _ -_-—._ where 3:1- is the right endpoint in [xH ,xE-j ? and where ex = I '-i i " i I . 1”. La———. _ q____wl . 5 6 b. Express the integral as a limit olsums: Isintlenuhix : Do net evaluate the limit! . . 2- I? ‘x 3’s” b u i . '55:} “I. 3 . n l 3 . . e- Evaluate Inn Z — — by ustng the Fundamental Theorem of Calculus. “WEI-=3 —5+3lv"n a e, _/ . ~ (iii) — r 1. ll}! W. 6. Evaluate the following integrals and the derivative in part e. ,- 2 .- - - . »- ' ~———~e i a? lez + will,“ l ’ _ “H; ' II . ' " “ __ '. 1 I ' . .e | I" -.i| ":‘L I? r , ‘ ' z i l bk I'- U' 9136 b5 l d 2 +1 a i i J {ix x x x I '_ If r-er' . ﬁle“; *I I L ___.__ ' .I III ._ .I'II E; arctanx __ II c; ft'x) = J'sin“ ma: L Etna-fax}-.- , ,_..- 2 a“ " .rri - ’ - l r __ ___._ If}: I If! a . H, .- .- II | t' all-1.: )l f2 - ' Ml lb ) a; LL T. Make a caiculus quality graph of f{x} = Are—*2” . Show clearly the [Ly] cmrdﬂ'lnles ofall relative extrema: and inﬂmiiun points, the .1: intmncpts. and thc bchaviur as 1—» {—ou and J: -r +un . .1. ...
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• Spring '08
• Shen
• largest Feasible value, sides ﬁfths fields, DI Fencmg mama, Cleaee‘ interval Method, derivative nfareain ﬁg

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Exam 3 - I I,‘-’ M t Li 1 Math 151 Calculus Emmi...

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