Calculus (With Analytic Geometry)(8th edition)

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Unformatted text preview: Math 123 Calculusl Name: LOW»; 5” ‘ Fall 2005 RWJ No calculators, one page of notes allowed Instructions: Read questions carefidly Help me award you (partial) credit by showing your work Note point values Check your answers if you finish early The exam ends promptly at 9:55 Good luck! /15 s \ /16 I45 —' . -. /24 Total / 100 l. (15 pts.) Suppose d (t) = 3t2 + 2t denotes the distance an object has traveled at time t. a. Find, and simplify as much as possible, the average velocity of the object over the time interval from x to x+h. b. Determine the instantaneous velocity of the object at time x. W = ZBCKH‘)?‘ Wm»): —- C336» 2.x) " k 4. my» [email protected]+2t) .. @@ A k \i 2. (16 pts.) Fill-in the blank/True & False: a. If Ei‘iflx) = f(a), [then we say thatfis (OIJ @000; at x = a. b. If f'(a) exists, then we say thatfis E/ f?” M WWW Li at x = a. [email protected] or False (circle one): If f is differentiable at x = a, then f is continuous at x = a. d. True .ircle one): If f is not differentiable at x = a, then f is not continuous 1 at x=a. 3. (45 pts.) Find the derivative of each of the following functions. There is no need to simplify. a. f(x)=(2x2+3x+l)sinx fax): (4m #3) 94:7: 4— (1%” 37¢“) 6“ 7‘ (x2 + 5x — 7) (2x3 + 8x — 9) 777:): Qt *5)(2-163+6*7c“?)” aha-Dams) c. h(x)={/4x4 +3Jc3 +2x2 +x+l 13- g(x)= my} . 41(7‘)=J§(4F$+97€3+ 2-»‘1‘ Fri) {(67:34 72cLH‘x H) d. r(x) = (x‘ + x3 +1)5 sin(3x2 + 2x +1) NIX): 5(x‘4—ch34- {)4 (st—x3 r39) in: {376‘ +17%!) 4- 4. (24 pts.) Determine, if possible, a numerical value for each of the following limits. Some of the following limits might not exist. E a limit does not exist, then give one of the following responses: A. In case the limit does not exist, but the function in question is getting large positive without bound, give the answer: +00 B. In case the limit does not exist, but the function in question is getting large negative without bound, give the answer: -oo C. In case the limit doesn’t exist and neither a. not b. apply, give the answer: DNE1 2 {ct-3) , ‘ m3 2 “gig—3 ‘ Q44. ( )( H- ,. A {:7 ~ ” x») 2“? x ) M} Q) a. b.1im3x2+2x+1 = 3(1) FLU/4’! x42 /,, ~09 d.lim— DNE x—bl x—l 1 DNE is short for “Does Not Exist". Math 123 Calculus I Name: sw’l’q” 4" L Fall 2005 RWJ». No calculators, one page of notes allowed Instructions: 0 Read questions carefully , 0 Help me award you (partial) credit by showing your work 0 Note point values 0 Check your answers if you finish early 0 The exam ends promptly at 9:55 0 Good luck., 1. / 24 2. / 16 3. / 15 4. / 45 Total / 100 1. (24 pts.) Determine, if possible, a numerical value for each of the following limits. Some of the following limits might not exist. If a limit does not exist, then give one of the following responses: A. In case the limit does not exist, but the function in question is getting large positive without bound, give the answer: +00 B. In case the limit does not exist, but the function in question is getting large negative without bound, give the answer: —oo C. In case the limit doesn’t exist and neither a. nor b. apply, give the answer: DNE1 1- .— ‘ a.lim2x2—x+3 :- 2(1) ‘2'+} 7 x—->2 b.1im 2Jc2.4 . y... W 1'. A (K*L) .2 x—nx+x—6 2"”- Qc+3)(“"’) «.42.. 00"» — ‘ DNE is short for “Does Not Exist”. 2. (16 pts.) Fill-in the blank/True & False: a. If f ‘(a) exists, then we say that f is E [PFFNW’nmU6 at x = a. b. If 9331‘“) = f(a), then we say thatfis £9”) 41 All-1005 at x = a. c. True o’ircle one): If f is not differentiable at x = a, then f is not continuous at x=a. ’1' False (circle one): If f is differentiable at x = a,' then f is continuous at x = a. 3. (15 pts.) Suppose d (t) = 4t2 +3t denotes the distance an object has traveled at time t. a. Find, and simplify‘as much as possible, the average velocity of the object over the time interval from x to x+h. b. Determine the instantaneous velocity of the object at time x. Q) gamma—n) ____ [Hwy-4.3m») -3.sz 3*) In 4. (45 pts.) Find the derivative of each of the following functions. There is no need to simplify. a. f(x)=(3x2+2x+5)sinx WK) ‘5 (52%“) mm 4- (“1442‘”) mac (2x3 +8x—9) . (x2 +5x—7) C57“ 4"?) (KW-61:4) " (1-2‘34-37‘~9)('1x4—5) PM (76‘4’65—7) 7" 0- h(It) = 5x4 +4x3 +3x2 +2x+l b- 30:) = Jl/x): h?K)=l' 3 L(fx‘J—fitxJ'f-3‘x‘1'3-KH)$(w'ffif'n-K 4-4764-1) d. r(x) = (x3 + x2 +1)6 sin(7x2 + 2x+1) / V/(x): 4(x3#X‘+|’)5Ox-zkvz$) “(77(14'1‘“) + (K3+KLkl)éZp‘yz_ (7K1+‘¥+l)j<l¢x+1) e. s(x)=tan[ 2x341] x +3x—8 a, Fifi“ 3 .5 5(6‘)= {CL} 7x34—K L<_______. 1*.“ 57‘ a 1“" 7‘5“? 3 16 +3x—g <2/x14~1)(k~r3«—z) » (7)8”)(7440) ________________________....—-«— CXQ‘J- 31v- 3') L ...
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