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mid3_practice_sol

# mid3_practice_sol - Problem 1[13 points Find the dimensions...

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Unformatted text preview: Problem 1. [13 points] Find the dimensions of the rectangle of largest area that has its base on the z-axis and its other two vertices above the m-axis and lying on the parabola y =q- 3:2. Mn ﬁne avecx Ts RM: —2—t3+\xt . Wm - WM = +0343 1? o<t<ﬁ,t\m~ {’(+3>o -——z ‘s‘ is I? Ji<+<3 , {’Ww Vc—tmo .1. F ts Aeneas.le Ync m 5 {mg {(‘tl MAC. ‘l'l/Ys AbSolM’le max 0+ i=5 TMus kl The Wcicmgle hows bus. 25 M Mtg 6 Problem 2. [10 points] Using Newton’s method with the ﬁrst guess :5; = 1, ﬁnd the third approximation 13 to the root of the equation 1:3 — 1: - 2 = 0. You can leave your answer as a fraction. Lax £020 = 17’- 7‘ ’ Z w {/00 : 3x14 Thus _ _€(K‘) xz‘ X' 'F’CXI') \—\-'2_ _ = v 3_\ — 2 13'2‘7- 2.. 4 t 2 - *f ' \ 3.214 \ .. V8 Problem 3. [14 points] Find the derivative of the following function. x” 89+: = dt 9(3) ./2‘ Vt + 1 Problem 4. Find the general indeﬁnite integral. (b) [5 points] 1%; y 66X 4 Siv— A ¥ = g”, \—x'* H" —l \v-‘Z. :2gwx+c — \ xcb< =30” DY AZ. [New C=§M+ﬂ+ C (4 + 1n z)2dz z (c) [5 points] / Lg+ w—Mﬁw [ (4+w\°‘ x '- dx (d) [5 points] [scc‘xtanzdx ke+ u: §€C\$. Tm du=§0ly '7; 3 4+J~Q gulch: —%+C=C 3 Problem 5. Find the deﬁnite integral. 5 (a) [5 points] / I122 — 2a: — 3|da: o xl—zx—g = (x- 33 OH 0 1? 03x33 , Hm» {Ta-\$30 L; 39({5 , 1w. Xl-IY'3-70 2 '5 ' WW SS [xi—u—ady:-g°&l.zxv\$\&y+ €33?“ mag O Y 3 3 . 5 x 2 t ‘ L—XZ-3X] + '2?— X~g>€13 3 o .. _ [apex —q -014, [E2 0.3—4? - (WK-00] ‘ ‘s g (18‘ is" - " _ q + ‘1: —LLO+“] _ 3 12 3 (b) [5 points] fol 29:33:23” Le+ u: e+1e7‘, T‘Mm du=(e"+xe" Mix: asxm (=3 esuéze ‘ X 2Q ° ewe" e w '26 _ QQMM‘X —: 12,,22 _ 2&2 = 1&9. Q Problem 6. [10 points] Evaluate the following limit. lim l(\"/«'a+ VE+~~+ n—ooo n , moo 3:1 \ .L V‘ n I : QHM 2:. e h who L'l Problem 7. A particle is moving along a line with velocity v(t) = t2 — 4t + 3 (tn/s). (a) [6 points] Find the displacement during the time interval 2 S t 5 5. S: Um d't " ingQ-Wcﬁl 1H 2 [t3 {7. 7 “1 i 1 3‘ 3 : 1.13.40“?- (7—946) (b) [7 points] Find the total distance traveled by the particle during the time interval 2 5 t S 5. S Tb-lrbﬂ dlg‘lamu c 5z I UC’éN = (£43 (#0 L? 29:9,, u(ﬂeo IQ 3§f€\$, we)?» Thus ,- Bx : — [if—aihsg: + 494%]: :— {qu‘a-‘ﬂ’L-gi'Q'l'Q] * ~§o+\§- (Ox—h? 40’) < \umlli = Sahiqugét + S (if—«Luna ...
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mid3_practice_sol - Problem 1[13 points Find the dimensions...

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