Calculus (With Analytic Geometry)(8th edition)

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Unformatted text preview: . ( .4.” 75.12,:1; " 1.. (14 pts.) Let . t; » - . f(x)=xf+2x’—7x2—8x+12 " f‘ a. Evaluate f(2) using synthetic division. In particular, fill-iii the blanks below 11::él and then tell me what f (2) is. I i ‘ AW»: b. Also determine f (—2) using synthetic division. I 2. - 7 - 9’ I z -3 I o -7 6 0 Abv=o c. Use either part a or part b, as appropriate, to give a polynomial which is equivalent to 4 3 1 11H;2ffl13 — «3—7x+4 x+ except at x = -2. ”I. 2. (25 pts.) Let f (t) = 2:2 + 5t +3 denote the position, in miles,rof an object as of timet, in hours. a. Compute f (0) and f(2). ,, b. Compute the average velocity over the time interval {0 hrs, 2 hrs]. Give me a numeric answer. = “Pk. _ c. Find, ands simglyfy as much as possible, the average Velocity‘of the object mm the time interval from x to x+h. (9/3“) Hx)_(7_(x+k71lfl+§(x+k)+33~ C27: +57€+33 =®[email protected][email protected] k $xh+u1+5k k H H d. Using your answer to part c, determine the instantaneous velocity of the object at time x. x . as, 47% “”5 = @ he» 3%(18 mypmsimhe blankfi’rue & Fm - a. If f’(a) exists, then we say thatfis~ DIFFWIMW ‘ tat x= a. b. If limf(x) f(a),§then we say thatfis 601917»)qu J i hat 1t: 0. c. f '(x) may, in one context, be interpreted as the instantaneous velocity at time x. It * also my be undeistood as-fiie" Slope»efthe _, w i of f at x. ' ~.. A. [email protected]" False (circle vone):'”if f is undefined at x = a, then it can’t be continuous at x=a. .e. True [email protected](circle one); Iffis continuous at _x- w a,_ then f is differentiable at x = a. fi'r False (circle one): If f is differentiable atx= a, then f is continuous at x= a. _ , ~ j- «s was“. .23» u; {saw _, ‘1 ~ -' sets: ' 4 (25 pts.) Determine the following limits. If possible, state you; was as numerical values (e. g. “5”) or 00, or —-oo. Otherwise, state “does not exist" as appropriate. . 2x—3 a. 11m = ”.3 71-4-5 243395 ,1 ‘ '1 ,3 t: r i "5.?ka b limx +2x— 3 ’ a (Ki3)6?c"l) 4 (K4) ___ i g i ”rs—3 x2+x-6 - (793)61'1) 6‘ > -5 x—M .314 e. lim[(2x:b-l)(tanx)]=-<1‘%-+ I) «(3. '11: -.—. : ix ”1" * z . ‘ ‘, ~'~'.' I - V' 7‘ 5' K. “w‘ ? 5.3, _ v 7 ~~=,nmm&fi points, sketch you; V_ - - ' , »(Note:l’1ixinoi “a formula”.fcrryo€uiig ' ‘ ' ...
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