ffi I Q II MM I VI I V2 I V3 I V 4 I :11 a a a e b Math 101, Final Exam, Term IANSWER KEY I : 1 a e b c e 2 a b a c d!


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1 Math 0, Final Exam, Term 3 IANSWER KEY I I Q II MM I VI I V I V3 I V 4 I : a e b c e a b a c d! 3 a d e d c i 4 a a a e a 5 a e d e c! 6 a a d e c 7 a e c d c 8 a d d b b! 9 a c d b e 0 a c a c a : a a a e b i a b e d a 3 a c d d d 4 a d b c C i 5 a b c d a I 6 a e d a e 7 a d c a d 8 a d c d e 9 a d a d e 0 a d b b c. a c c c e i a b a d e IE' a.e d d e 4 a a d d a L.::.:.. 5 a c e. a c ffi a a c e a I 7 a c 0.. c 8 a c c d a I "\>
2 King Fahd University of Petroleum and Minerals Department of Mathematics and Statistics Math 0 Final Exam Term 3 Sunday 9//03 Net Time Allowed: 80 minutes MASTER VERSION
3 Math 0, Final Exam, Term 3 Page of 4 IMASTER I. An equation for the tangent line to the curve y atx = 0 is xi x+l (a) y = xi (b) y=3xi (c) y = xi (d) y = 4x+ (e) y = 3x  x. lim x+l+ "';x + t( ~m (a) (b) 00 (c) 0 (d) (e) _\ ot )en o ~ (7 ~ ) 00 ::r :=.$0 \\VV\ === "j...'f \t F+I _o(j
4 Math 0, Final Exam, Term 3 Page of 4 imasteri 3. Where is f(x) = In(  y'x) continuous? \n Hs do m~ ; (a) [0,) \., {X ) X?''..) _"" \ 'J X / n ( y)<."/.r::: > ~ <. \ ~') x < ~ (b) (0,) (c) (0,00) Ccm.bll'IYlj, \jje ~~ o!sxl..\ (d) (,00) (e) (0,00) l'\  n... n 4. f: (~+ k) = Z* ~ak.. k=l n K. = f\ (= n...:::: \( + al _ i. L ~ k. ::::)  n I<~I,.. Y'\ '\ (Y\+I) (a) n +n+ + ~...~ (b) n+n 3 = '" (c) +n ~+Y\~~ n (d) _+n n n (e) n n+ + ntv\~l)
5 Math 0, Final Exam, Term 3 Page 3 of 4 IMASTER I 5. The slope of the normal line to the curve y3 + tan(x) = cos(3xy) when x = 0 is.. X=o (a) 3 (b) (c) (d) 5 (e) If lim f(x) ~ 4 = 5, then lim x f(x) = xt3 X  xt3 +b9lt == 5 AI \'ly\"~ \'W\ "3 Q~ '.. (.. )C~'?, (a) 'VI ().~ \ \l'i\ (.\' od 4) == (J (b) 5 ~~3,\~ ~\><) :4 "fl3. (c) 0 =, . 3.l.\ (d) 5 (e) 4 rhw» \' "m 'i.~s ;r+6<)
6 Math 0, Final Exam, Term 3 Page 4 of 4 JMASTERJ 7. If f(x) = 0x + tanx, then f(3) (x) = ' ;f 't<) ~ 0 X I~ S~c.. X. f('v)::::?o+':l. (a) sec x(sec x+tan x) I, J.. ;{ seo( ~cx~nx." _ 0 + s.ec"x.fc:tnx  '. L a s..eck. # (b) 0 sec 4 x + sec x tan x tt, S ( '.. X SR<: x + 'Jl'lt\)( J., I Ltdr '><.f he} ~ O ".s.ec~ "" r' (e) sec x(sec x  tan x) 8. Let H(x) = f(xg(x) ). If f(4) = 6,'(4) = 5, g() = 3, andg'() = , then H'() = '(:;r lx) ). L'::i <J' (xl  ~('X)J HI ft.) :;. f ~ (a) 5 I [:cj()+:)cz)) H'() :. f (J.t)c z.j). (b) 6 := f I ( 4) ~ [a(.) + 3. J (c) 0 ';:, _ 5 (4+?:» (d) 5 (e)  5 (I) )
7 Math 0, Final Exam, Term 3 Page 5 of 4 jmasterj 9. Using a suitable linear approximation, (.000)500 ~ (a).0 (b).0 (c).0 (d) 0.00 (e) \ e6 0 = It \00.:'>;::' = I + To = \~.o x 3 + x  X  : I 0. Let f(x) = 3 If R is the number of removx x able discontinuities of f and I is the number of infinite discontinuities of f, then fix) "",y... 'L (x+..j _!X+'Z.) ~ X (')(L_\) (a) R = and = (b) R = and = (c) R = 0 and =3 (d) R = 3 and =0 Q<f L ) (x I) ~ "X ()( I) (X+L) (XI) (xti) =~) ~+,'l..  I x 9'(.~ :!,.I (e) R = 3 and =3
8 Math 0, Final Exam, Term 3 Page 6 of 4 IMASTER I. If Newton's Method is used to estimate the xcoordinate of the point of intersection of the curves y = sin (x + ;) and y = In(x + ) with Xo = 0, then Xl = "T\ f (x):;: \Yl (x..r.f)  SIf\('X+ ~ } pi. (a) 0.5 (?<)  x..+~ _ CoscX,... "'i: ) t (Xol (b) 0.3 ::>; = 'Xc,  f I(~).\ (e} :::: 0 (c) 0. ::: o  f/(o) (d) z. (e) 0. l. lim (../x + 3x  3Vxx) = x+oo (a) 00 II tr\ )(~ 0iJ (b) 00 :;::;. c0 Ixl ( ~ \+ ~ (\.3). )  3~ \  ~ (c) 0 (d) 3 co (e) 4
9 Math 0, Final Exam, Term 3 Page 7 of 4 IMASTER I dy 3. If dx = cosx  3 secxtanx and y(rr) = ' theny(o) = (a) 7 (b) ~ 4 (c) 3 5 (d) (e) 4. A hot air balloon, rising straight up from a level field, is tracked by a boy 00 m on the ground from the lifting point. If the balloon is rising at a constant rate of 50m/min, then the rate of change of the boy's elevation angle (} when II 7r. v = 4 IS cj ~ _ 56 mlm,,, dt: (a) 0.5 rad/min (b) 0.0 rad/min (c) 0.05 rad/min (d) 0.05 rad/min (e) 0.5 rad/min
10 Math 0, Final Exam, Term 3 imasteri 5. lim ( + x)~ \'" (\+:,:9 Xl>OO \ \ '\ (\ + l,:x) :.  Z \ \i\?c.. In ~ ~ .\\"\)(' \.,(\+ x...,) (a) J \tw \" J := ~~...." (b) e (c) J (d) e (e) \ .. Vz e 6. The absolute maximum value of f(x)  sin(x) + cos(4x) on the interval [0, ~] is equal to (a) 3  (b) I f("i<):::o (c) 3 (d) v'3 (e) + v'3
11 Math 0, Final Exam, Term 3 Page 9 of 4 IMASTER I 7. (b) yin 0 (c) yx In(x + 0) (d) yx(x + 0) xy (e) In(x + 0) ex 8. The graph of f(x) = X e + (a) is concave up on (00,0) (b) is concave up on (0, 00) (c) has two inflection points (d) has no inflection points (e) is concave up on (00, 00) X e c "'.)( (e+i)~ e (ft it~ ) (ex+) ;. J J II (x) =D ::}e" ('/ up o d<3>v,,\ t ty't\.e. \(v \..ectlvn. t
12 Math 0, Final Exam, Term 3 Page 0 of 4 IMASTER I 9. Let f(x) = a:x + /3x +" wherea: 0, /3" are constants. The value of c that satisfies the conclusion of the Mean Value Theorem for f on the interval [3,7] is (a) 5 /('><) = ;{on< + ~ r CC) :! (b) 6 Q,c(L+~   (c) 3.5 (d) 4.5 (e) 4 ~d c +Lfp.:zrolc..\'() ~C:~) i3,., ) t _ ('<;'" t f3 +Y)  (0.x+'~ Lf = 400( 400( c.:: ~D( ,.'(f == 5 I 0 to, 0. The number of critical points of f(x) (x  X 3 )/3 is <.f/'5 t) f I i ( x"}),( t  :,:x J (,.) =  3 'X (a),  X t I_~X   S3 5'('.) =.0  (b) 3 ~/("y') ONEb (c) 4 (d) 5 (e)
13 Math 0, Final Exam, Term 3 Page of 4 IMASTER I. The function f(x) = x44 x3+ 4X + 4 has (a) a local max at X = and a local min at X = 0 and X (b) a local max at X = 0 and a local min at X = (c) a local max at X = and a local min at X =  (d) a local max at X = and a local min at X = 0 and X = (e) a local max at X = and a local min at X = and X = 0 f ),,..."S _' X'l.. + '6'X... (~) ::. '...A S, :4':(( rx 'Z.?:'x+z) \ 0 :::: 4): (XI) (')('.) /, /> ~ "./ WI,y\ YI'lMC Jf('i) :: C :=::::) x::: (};) \) l hi'>". The function g(x) = e; is (a) increasing on (00,0) and (0, (0) (b) increasing on (00, 0) and decreasing on (0, 00) (c) decreasing on (0, (0) (d) increasing on (0,) and decreasing on (, (0) (e) decreasing on (00,0) and (0, (0). :z. ( 3 6<).: e X IlL I >D ~cjj X;fQ ~'  t 0 /' t?
14 Math 0, Final Exam, Term 3  cot X) 3. Ify tan ( ' then y' + cot x (a) ~ esc)<. (b) 0 " Q C'5.c. )< '\ (c)  ~ +. Ctj!;)<. + (~::..., = G:Cot x)"z.+_(\(o~y.. "'l ~ +.\_~e t. :l al f'( ::: esc x (d) csc X :: :::. ~ C>c.)< ~ :) L \+ (at )( (e) +csc x <. 't. ~ (tx + Cot ')( 4. A rectangle has its base on the xaxis and its upper two vertices on the parabola y =  x What is the largest area that the rectangle can have? (a) 3 (b) 30 (c) 0v' (d) 8V6 (e) 8 A=?::~ A (x) =?( (P~ 3 _ ::.4 x  'l. x.. I ~4 A (x) :::?L = ']. ,) AI ('<) = ti AIr (x) = _. x..., f\ () G 'x.. ~ (?} (\~4) :: X ex ~ 0) AII( ) :: _4 (Ii.<.. CJ { >(Y\ oj'/..
15 Math 0, Final Exam, Term 3 Page 3 of 4 IMASTER I 5. ( X) Ix ~+ dx= x (b) ++C x 8 X (d)  x  ln Ixl + 4" + C (e) + (In Ixl)l + 4 x + C x 6. Using 00 rectangles of equal width and right endpoints, the area below the graph of f (x) = 4x 3 and above interval [0,] is approximately equal to I:::... '.0' 'x =: 0 + Ln k :: ;:; bx ':: ~r;; t:. '/ ( a).00 A  L ~ ('X~) [) " (l  I(:..=" l"\, \<)~,.., k.. L =..:::::::; "" \''' \ Y\   c) ~L (b).0 "'" ~ _, "~Z\ J'..  " k 3 =:4" l'y\c;+')  ~ ~ V\. () C 03  '4 ' =\ '\ ".. (d).0 :::: (n +~) '= (I +~ ) ) L ~) == \,0\ (e).00 Alto  ( + ''ll I _.0. 0
16 Math 0, Final Exam, Term 3 Page 4 of 4 IMASTER I 7. If the curves y = x + bx + a and y = ex  x have a common tangent line at the point (,), then atlb+e = (a) ~ 0 (b) 4; (c) 4 (d)  (e) 3.So. o 8. If a is a positive real number and then a = (a) 6 (b) 8 (c) 4 (d) 7 they) \c (V'\ ~) '" eo. :l..j 0{. ~ 64, s;.; "So 0\.::: G (e) 9
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