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MAC 2233 Final Exam ReviewInstructions: The final exam will consist of 10 questions and be worth 150 points.The point value for each part of each question is listed in the question, and thetotal point value of each question is listed below. Only a basic calculator orscientific calculator may be used, although a calculator is not necessary for theexam. NO GRAPHING CALCULATORS OR CALCULATORS ON ADEVICE (SUCH AS iPOD, CELL PHONE, ETC.) WHICH CAN BEUSED FOR ANY PURPOSE OTHER THAN AS A CALCULATORWILL BE ALLOWED! The concepts and types of questions on the final examwill be similar to the previous tests, previous reviews, and this review, althoughthe numbers and functions may be different on each question on the exam. Thequestions on the exam will be taken from the previous four exams. Each of the10 questions can be found in the following places:1. Exam #1, Problem #2 or Section 1.5 (18 points)2. Exam #1, Problem #6 or Section 2.4 (16 points)3. Exam #2, Problem #1 or Section 2.5 (8 points)4. Exam #2, Problem #2 or Section 2.6 (12 points)5. Exam #2 , Problem #5 or Section 3.1 & 3.2 (24 pOints)6. Exam #2, Problem #6 or Section 3.3 (8 points)7. Exam #3, Problem #4 or Section 4.3 & 4.5 (12 points)8. Exam #4, Problem #1 or Section 5.1 (16 points)9. Exam #4, Problem #2 or Section 5.2 (16 points)10. Exam #4, Problem #4 or Section 5.4 (20 points)
1. Find each limit. If a limit does not exist, explain why it doesnot exist. (6 points each)(a)limx-tl\ iV ),. , b-; .\ -- (----. } -II'M ti -t;)\ix-'},-MJkt3 - 'X. ,--vx 3 - 2x-IX .?, -Y():- I) Ch ? t:;).) - -- fjH - J. --Jl{- Q()l- \ fi"t-d X4--/-L -.[l(b)"I1mx2 -x- - 4 X -6I- -10 -5(c)limX -2 -lif\')'(., - 2 x"II m - - x- -2 (x 2)2)(t!nY - pos - J-X - ?1 Alj t2):L :::-00::.-00-- 0! (JiH :l).j ;L0INkJuMI rkil"\-I-J:1L:.l
2. Find each derivative. (8 points each)(a) h(t) (t 3 - 4) (4t 3 - 2t2 5)(b) f(x) ! t' (l();::( lc -5') (3) - (3 \( -SV'I)( X, s)2::.- 12x- l - (/2'( - W) \ y-s-)'"-' - IS- -.,0" -010(h:- S-V·
3. Find slope of the tangent line to the graph of f(x)at the point (5,2). (8 points)-f (X)- ('/--G,x 4)'"-r' (X \ ( . -Co x-r ( . (2'K -iJ,)r i. (2'-f' ( ') : : (S'-- "s 1-\ ( -30 )- , (10 -Co)- (yr t. y---"::::. l{ f\iy ' d-'i--. -- S-- )ill Jx2 - 6x 9
4. (a) Find the second derivative of the function h(3) 33 (3 3(6 points) t{ ) Cos5-I(os --43 -(os[!" (s ) 305 -lfgs - Co](b) Find the third derivative of the function2x. (6 points) ( \ J'f.'b '{3 -2x.f '(X ) lOx 4 12 x:z. - 2til (X):: 4Dx Jl\xf (x) 2x 5 4x 3 3) .
(a) Find the critical numbers. (6 points)-f'(X) ' '-(" ')-{2X'-)j'){ .) - /Dlx -(qX4-32.l(:4 )"l-"K'-4 32 4'(ll/2x 4 -g yUZk kl.lW(k 3T 9) :"-J4'x. f3l(k'-lX3T (X.J.,()(X2.J X"' )X3 )(3-f '(K) t,'"J ·J0 fO(x oJ(b) Find the open intervals on which the function is increasingor decreasing. (6 points)m:, pos ;yOr ', ri(kx:::: --3:II : V'IV\.1(':: -I',lIT : fiG x I'.'\ flLreASi1 '. ' '(-3) 'It(-I):::(1'')::.;.:g-f; : :J ! : : pOs( (XJI - d) U (0) (0)J.tc.CUl s', : (- i}. ( 0) pos
(c) Find the local maximum and local minimum values of thefunction. (6 points)·.("(x) t"'1 \ 'lV\tr i1ckc.(( \"j-t.-boJ-- VtX--()., 80ofx. -J, So j'i 0.tel ) s 1.mJ at x- -- J . (-ir a(-l\ -g (-8) - - ,- rfa-- 6 -}- y J[-d-)'Zilur.J) ::00VWN(i:; ('-t)- 6 (-Jr -3)J0. CJ 1l. t"fM50', I. c. I r 4Nt:orn MM v\ ](d) Find the extreme maximum and extreme minimum of thefunction on the interval [-4, -1]. (6 points)txtrl : (-;),- ) rtJN. \'" '.(-\t, -.!})[ ""'VI.
6. Find the inflection points and the open intervals on which thefunction f(x) x4 - 6x 3 12x2 7x - 6 is concave upward orconcave downward. (8 points).fII(X-) - 12x z::3(0)( - I [X'- 3X tJ.) 1:2. (X -02.')C )(-1)t (X- ') (X-I\.:: D1. :?ic.t.'1 ::::0 " -\'\I(0) (po5)( )(JJ- Jr Pid x:: ;', -f (;) CfOS} ("j)( peS)'fIIr.s :-J][: 'Piel x 3', ·fl C3! -.: ( FJ(pos)Ceos) p05CiN\CQ.vt '. (- )0 J ,) u((;l, ') CAve. ', (/,,,)
7. Differentiate the function. (6 points each)(a) f(x) in (V4x .f(X k6)I ((l{ Ho) I/ )--Ii 4tH"\-. -- . y;; ttt
8. Find the indefinite integral. (8 points each)(a)J(4x J X - s JXrk. JItNxi(4) - s(tl H C[X - X rltCJ(b)3-5x l)dx
9. Find the indefinite integral. (8 points each)(a)(b)'l\.;\- - J\A 3:; "Lol:;Ju? oI " Ju-s;) -l\J:L.-y c.
10. Evaluate each definite integral. (10 points)(a)3L toW - Dd0 i( )- k I X -l I: :: [l -:21-( I -Il [ - J1-[H1(b)13(y 3)2dyU::C J :S iu ::: r:' 3 : Ct -:: -t 3 ::. rO d- -O : U: -o -\-1 u\k -" 1Co-3- -:3- -3dlb:::. ;;t - q :: 3]
MAC 2233 Final Exam Review . Instructions: The final exam will consist of 10 questions and be worth 150 points. The point value for each
