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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) $5:
(CC) (2 pts) Find f’(~1) v»
(dd) (3 pts) Find f”(~ 1) w (ee) (2 pts) Which one Is bigger, f’ (— 6) orf’ (— 4)?P (M {Q (ff) (1 pt) is f (m '3) positive or negative? Nézhﬁﬁ ME; (gg) (1 pt) Is f’ (— 3) positive or negative? 9333‘?” WE (2) (75 points) Find the foliowing limits, if they exist. Find the infinite limits as
' well. (e) (5 pts) limmg w‘” (f) (5 pts) limx+m el/x (h) (5 pts) limxam e‘xsin (x) N‘Wﬁ iwawwxcwww Mim 3 \
(m) (5 pts) limxﬁmm 5" +7 :2. Lm (n) ' (o) (5 pts) limxwm (x3 + x4 « x w» 96""1, ifxsz o { z
(10 pomts) etﬂx) ex~2, if x > 2 .113.) (419158) Find limH f(x) A$ 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» oneX ~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 melodyK3 Rcm es; 1&9 we r" (*0 l 2“ 4 !
53(123u4b 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 lweo . ___ (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\OPC1 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 Kit9n) ”:5“ [2 ﬁlm wg+k) “Bi—m
i990 in heo (x m x ﬁég‘o 6de T f 3;:ng MM)»; 5 iiiyo (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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 Spring '08
 Guzman
 Physics

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