finalsols

# finalsols - We u 1 Evaluate the following limits(1 point...

This preview shows pages 1–8. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: We: u 1. Evaluate the following limits. (1 point each). l, sin3t9 km {l" 36 KIQ COS Y9 ' 2 1 ; game-940 39 sme y L/ a, x \‘x k l/ \ ( l . LI 332—1 . hm (iv/00ml) r, hm ‘ 3:qu x—l x31 x~| x— t < ) 2 _ ac — 1 l' 11m = “"1. z—r1+ (a: — 1)2 >0“ . 1. 11m —smz= z——+oo.’,L‘ \fx+h———\/—z—1_ mm W , h ‘ 2. (5"!)[Y'l — I’m '2. —— :00 (/70 LY SiMPEZ—e (g Q i X 5}” K W44]?! —”l_?0 (’7 \lxrA-l +J7Q »<+A~( —-(s<-'!) a um i r “ hat.) Uxmq'ﬂ/KT? a lim h—>0 a (ll/V) f M L‘—)0 L,(.l)¢h~l +t/K’!) am 2. Use the deﬁnition of the derivative to ﬁnd f’ if f = 32:2 + 2x. (5 points). Hm gym-H'iEL) 2 lino 3(X1—hr1—2(xrh) ~3yZ—2x ln‘m in H90 k (1m CXk+351+2A [m logo A :L,(~>o (6x1'3L‘f2) : éxfz. 3x+1 a3<1 3. Find a, I) such that f = (1102 + b 1 S a: S 2 is continuous. (5 points). 6 — x3 2 < a: "M snow, if} wab = F“)- Y“?!- Ifm X~> ' 9'64): 4. \ ; 2 “a 5 ’93-), 5:3; m: —2_ 7?) 5% cpnfil ﬂue/yﬂu‘ﬂ) on each h‘ne abut/e WW5" be eciuqu (—(:q+5 -2,:L‘a+b \UQ Subf/oc‘l' 4. Find the point(s) on the graph of f = m2 + 1 Where the tangent line passes through (2,4). (7 points). ¥‘(X): 1% / 50 “>de7 )3»! (i'ﬂc’j wukrm bevwepn ( X/ x1+\) Omci (21W), S/a/DE 2K / ‘1‘ 9 ZXiLJLLL 1‘)‘ 3 or 5. Find the equation of the normal line (line perpendicular to the tangent) to \$312 + 2y - a: : 2 at (1,1). (6 points). d ,. “witty”? ‘i-Z—I '0 {3&7 M ((,I.)3 d d 2 “I 1- +2 .1... 3 z) C(Y / M I o TX :0 So fat/96"} hm; is Lori ganfd/ So ﬂo/ﬂmi line is ire/Hm (‘ TMQ Jeff/CG] “HQ Pc5Sir7 (ill) X:( K (73’ would 69 Molizonmklj . y 6. Find the following derivatives. (2 points each). Dx[a:sin(2x2+1)]= X cos(2x2+i) + Si/l(-Z)<Li~l) Dm [cos(sin(x))] = ~5 n (5; a X) C0 '3 X D [ 300w ]_ (44 SM ><~*) (‘35MX) ‘ 71a)st I (WEAK—{)1 4sinw — 1 7. A particle is at position s(t) = t3 — 22—1t2 + 3015+ 12 at time t. It momentarily comes to rest twice, Find its acceleration at each such time. (6 points). v (6): 5m: 36 ~24t + 30 =3(€~— 7t+/0)=3(t“2)(£~s‘) Comes +0 r951” whet“ i=2 or {25‘ C((ﬁ): S”(€> 26f. ‘2‘ 8. Use differentials / tangent line approximations to estimate \/ 121.1. (6 points). Let y : J;— “Gaeid Pro" ((21, 1:) ~ clv _ .L ’ Eli ____ __l‘ E; ” 2‘}; dx “m N 21 ﬂqh line :‘l(x-(2() 9. 10. Water is being poured into a cone of height 12 inches and diameter 6 inches at a rate of 10 in3 per minute, but the cone also leaks water at 2 in3 per minute. How quickly is the water depth increasing when the water depth is 5 inches? (7 points). 3 3 What is the largest area of a rectangle with two corners on the :c-axis inscribed inside the parabola y = 16 — x2? (6 points). D 3 Co, q j x2 11. For = m2+2, down, has inﬂection points, critical points, local min, local max, asymptotes. State any symmetry of H. Sketch its graph. (11 points). ﬁnd where H is increasing, decreasing, concave up, concave We: 2mm ' 1*} 2* m-: A (\$4 +1-)2~ {Walk I H ()0 >0 whom ><>0 ma: (0,“) H’m <0 mm Mo decr (-“°(°) ,—>o~ (’x‘)-co 6’ 50 Y3( '(s q Lodz} zomr —~ W (531-2) HUM 1% {9 ; XY+HX1+LQ~§XL1~MK1 ’ :“XWZW ., \ Y __, 1 r. ‘” v?» (3 1+9 1v {X l “ 1)q (leerl >( x H//(><l30 => Xi; Hybmx ~“(tS’ A 3 6 R g 3 “"3 12. Suppose that if a business sells :3 units of squash, it has revenue \$4 + 4x2 and total costs of x4 + \$53. How many units should the business produce to maximize proﬁt and What is the maximum proﬁt? (10 points). 3 X P: Proer :— Reumue“ C0“ 2 lez” ‘3' D: [0100) Filx): gx ~><2 :0 =7 XlS’K)=O =>X10 or x= FII(K) : 8 ’2X/ Fl/(O): ? >0 I 5'0 O ’P”(8>=-sz<o Wé‘o W ,x‘qulos may % (SW? M CWWM “Wild/"r5 NEW—25o 53%? 1:11, PM: ~09) l-e The busing» manual sell 8 qnl'rs (w 67“ Q MK meﬁnk d; 1:55 7 13. Evaluate the following antiderivatives. (5 points each). 3 /(x2+cosx)dx= 2—; +54% Xf‘C, facsin3(5a:2+1)cos(5m2+1)d\$= (7'6 Sngxafll “LC, Le} Q: glow—KIM) do : ﬁx Cd\${§><l*~‘)d>< )9 ‘2 X<OS(9X “ldx: % du § I , l I? g 0 {X 9”“ng F‘>C05(5x Hid“ : éiuiclq :LTlOCAL/f—C l L : 95 §inl(§><z+()7¢(f 14. Use the Mean Value Theorem (MVT) to Show that f = 51:3 + x + 7 has exactly one real root. (Hint: Try showing that it has at least one and then showing that it has no more than one). (10 points). 70,; (pm, am, 9 NW“ ma fur (rm as my: 63/1 0,47 1h berm, )K/w‘e ﬂ-w) <0, \$00) > 0 So“ £97 TI 3N ‘(“(0,(O) 5.t~ :O. rIf we and” warm" ropich Mumbws, coach Say (I'm x—am 79M 2 ~60 , 50 70 MWMW <0 1} Kﬂmoo : Q>0 5'0 @aowf’aaﬂr >0 M ‘0 r wk and P/OC9€C( Q5 aka/Q w’lbovgk Var/1M7 abbot w? ‘ ' ' 2 pm 0 a /; Q XQCHy 'p .3" 130\$ 1L / {1070 we ‘4 7’0! (45 10 Am; a 7L /eas+ a n e [cad ‘ MOM 10m mmwv mics xt Min hm‘h) Le 9593” REFO‘ I m Mm, 31¢eron 5+ ﬂcr—M 50 ymza (BL/(Jr \$‘(C52 3C1 +( is never 26/0 (Wu'n Uq/ug ,‘5 (I) go 1mg "(3 ;mfoss§~‘>“°~ Th“) 30 C(oc‘s “07‘ have MO/e fact” one rec-1+. .-‘ ﬂ [4&5 €><0£Cf(\/ cane mgof‘ ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern