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Exam1_Solutions

Exam1_Solutions - MAC 2281 004 EXAM 1 Name SOLUTION 3 The...

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Unformatted text preview: MAC 2281 004 -- EXAM 1 Name: SOLUTION 3 The exam is out of 150 points + 10 points bonus '3 160 points. (1) (40_points) Answer the following questions for the function y = f(x) whose graph is given. (a) (1 pt) “me f(x) 2 1+}, (b) (1 pt) isfdefined at x 2 ~51: If yes find N45). W: 3. ) (195)325 (cl (1 pt) limxfl ftx) 2 o (d) (1 pt) is f defined at x = *2? If yes find f(~w2). NO (e) (1 Pt) limx—wa“ fix) 2 +616 (f) (1 pt) limx_,;3+ f(x) m .1 $43 (g) (1 pt) 11m for) z 24 (h) (1 pt) limxul f(x) = 1‘33 (i) (1 Pt) “mac—>5 f0?) 3 “1"6‘359 (1') (1 Pt) “mac—>7" f (x) = ‘15 (kl (1 Pt) 1imxa7+ f (X) = Li“ (I) (1 pt) lim9H7 f (x) = Does mm" mm (m) (1 pt) limxuwm f(x) m 1411 (n) (1 pt) 11mm for) = :s (o) (2 pts) Find the equation(s) ofthe vertical asymptotes. sexual?) N13 x22? 5 (p) (2 pts) Find the equation(s) of the horizontal asymptotes. K6319 AME" 844:3 (q) (1 pt) isf continuOus at x :2 *5? N63 (r) (1 pt) Is f differentiable at x = —5? NC) (5) (1 pt) ls f continuous at x = 1? ”2‘5“”; - (t) (1 pt) is f differentiable at x m 1? No (u) (1 pt) isf continuous at x = 5? MD M (1 pt) is f differentiable at x z 5? NC} (w) (1 pt) is f continuous at x z 6? WE; (x) (1 pt) is f differentiable at x :2 6? 11115:) (v) (1 pt) is f continuous from left at x 2 7? WE;- (z) (1 pt) is f continuous from right at x m 719116 (aa) I (1 pt) lsf continuous at x = 7191111”) lbbl (2 pts) Find f’(2) $5: (CC) (2 pts) Find f’(~1) v» (dd) (3 pts) Find f”(-~ 1) w (ee) (2 pts) Which one Is bigger, f’ (— 6) orf’ (— 4)?P (M {Q (ff) (1 pt) is f (m '3) positive or negative? Nézhfifi ME; (gg) (1 pt) Is f’ (— 3) positive or negative? 9333‘?” WE (2) (75 points) Find the foliowing limits, if they exist. Find the infinite limits as ' well. (e) (5 pts) limmg w‘” (f) (5 pts) limx+m el/x (h) (5 pts) limxam e‘x-sin (x) N‘Wfi iwawwxcwww Mim- 3 \ (m) (5 pts) limxfimm 5" +7 :2. Lm (n) ' (o)- (5 pts) limxwm (x3 + x4 «- x w» 96""1, ifxsz o {- z (10 pomts) etflx) ex~2, if x > 2 .113.) (419158) Find limH- f(x) A$ xwai: X< 2 (AAA 50 I? (X)':;)<»~in <33) Jain”! ”900 2:; «gimm(X-|‘) "32""1 3E] 24% :2“ >992, (b) (4 pts) Find limxfi2+f(x) + > , xm—ZL A55 Xm'vBQ. ) )8)“; Canal 30 {260$ E _ 1.... -, \ P—2. 9.. 0 WM Sq «Qim ~9C><§t£sam €32?1 2-: g :6: 2: :L] (c) (2 pt) Is f continuous at x = 2? $7:an %$“¥(X) ":1 LL 2;. QQL+¥U) , ' ‘ I. X :31... flew/gfwa $§fl¥£ > At 54:2”; £5“)? .4» one-X ~59 fCfiL): 1'4 '5: 1L {ijfl gig): $025 ,2 ‘t‘lkegerpwrfi Shae; xefl. _ {s mn‘finmus (at x222, (4) (10 points) The displacement (in meters) of a particle moving in a straight line is given by s 2 1:2 ~— 4t + 5, where t: is measured in seconds. (a) (5 pts) Find the average velocity from t m 1 to t = 2. A‘Ei‘tuiyl 5'31'2"~1+»l+8:lmu+821 N: we stziwwemR—r—RHSM we mamas melody-K3 Rcm es; 1&9 we r" (*0 l 2“ -4 ! 53(123-u4b 2: Que h m m m IL m:-l:er%&md§ (b) (5 pts) Use the definition of derivative to find the instantenaous velocity at t-— -— 1 Vli): e I \ SCl la)»- 5(4) (1):; Rm WLKMW lw-eo . ___ (10 points) Let f(x) m \/x + 3 (a) (5 pts) Use the definition of derivative to find f (6). :2wa iifljfl WQT WINE Me):— Me - r h .._. ’51 V W 2; fl:_§w. -‘1+in..+ ,ngmmkm +RWWMW5 hgo 1" W + (b) (5 pts) Use part (a) to find an equation of the tangent line to the parabola y = Vx + 3 at (6,f(6)). 53(6):" \Jé; +3 :thz 5. We Eonaeit Una PCk‘DEBQ: Unmuak (6 5)) S\OPC-1 I53 M: $16)": We efimfi‘afi of? Eng 'Emaer'x'c time: is; <33 ;.(6) (S‘pOints) Find the derivative of the function f(x) = 1 Being the definition of derivative. i i _.1¢“*-<=x>:,tm ~ MW» a: in mm ‘ ‘5;ng h , hero 1" _ I ' X M. Q? +\"‘Lfim X 5, (X444) 2% .Qjm Kit-9n) ”:5“ [2 film wg+k) “Bi—m i990 in heo (x m x fiég‘o 6de T f 3;:ng MM)»; 5 iii-yo (my): Hwy" X'x 5., , x2“ (7) BONUS (10 points) Find the horizontal asymptotes of the * Zex+3 curvey ~— elf—1 _ 2. x E) '3 I I '- x . £3: + m)? t 1+ g)“ ._'-'- .26: +3) __, \ e W? - M 1 _. ...
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