math161 s07 midterm2

# math161 s07 midterm2 - Math 161 Midterm 2 Name\5 Date March...

• Homework Help
• PresidentHackerCaribou10582
• 6

This preview shows pages 1–6. Sign up to view the full content.

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

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

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

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

Unformatted text preview: Math 161 Midterm 2 Name: \5 - . Date: March 2, 2007 Instructor: Dr. Paul Choboter Time limit: 50 minutes Read all questions carefully, and show all your work neatly. Calculators, books and notes are not permitted. Good luck! Question Score Points possible V 1. Find the derivative of f{m) : 3:32 e 51“ + 7’ using the deﬁnition of the derivative. (In this question only the differentiation formulas earn you no points. In all the other questions on this midterm you may and should use differentiation formulas.) £00 3x2 “EM—1 5? (K3: M“ 3 mm: - 5 LX+h3 :1 “"sz bot—U h—vo .Wm—m ”gun-IF' -'—‘ Q 0‘3 £190 X+bxh*éhl%"5hﬂ*%ﬂﬁ V -_ 1 V 2. Find the derivative of each function. (3 pts) (a ) f(:c)= —3:r:4 +%+1 .7 my} \$00—— .gx4+2:x r” ”s W): -—m3~x 7» / r : .— 9— 3 -—- ___\__ H (x) \ wk ,7 "fr—X3 J (3 pts) Lb) f(:c) ;. \$13283 ,5 1 - ‘ , iJF’QO= ﬁe“ 5% l’f/ \$111 .I‘ 5f" 2?? o\ x?) 7 C 3 -;——-—t::) a); MW ‘3 ii Cx)‘ ~ L (”2) ELK" 5X :jgllcosw j (3pts)(c)f(m)=(1+\$3)1/3 # (3 PtS) (C ) HI )= 7“” ‘\ (¥)_ fl COSXX Coo mm W \$2 (03“) ) {T/GC) %7 7mm“ (“00‘ D 5% K: _W_ £766 QM 1(0306‘) - — _ V f“ L: W D QODOM x3 n07 cost“) ”— 2 dy V (5 pts) 3. (a) any“ +332 y: a: + By Findd — in terms of H: and y. ﬁ CX%4+X1®: QC+3d\j)&( x3w +LE§LX+X€1XUJ ggxx :\+3%& x4l5a%*\5+‘*ai aﬁ-‘Wﬁ 5/ x‘bﬁg %% + X2%%—*3%&14—LA1X dJ (5 pts) (b) Assume that :r and y are differentiable functions of it. Find —T— when 3:2 +1312 3 25 dt d '2 7: [’1 23C: Mﬂafﬁ 2K% +2kjgi\$zo d M M3? —. "”7:— 5 _,_ d 0C a a? "' :%”(“13 V— : (—0—— 3% (\$1 ——57: V (4 pts) 4. (21) Find an equation of the tangent line to y : I + \/:1_: at :1: 2 4. \j I» (a \5 2‘. 7Q 4r \IX \5‘; 4+r: 4¥11bﬂmmy€hml q \jmﬂx L \Lﬁﬂo 2%;(x 4 Us \ﬂ‘:\+.\ix 1 ........ _.._._.——- ______ __ — n. \jf—l 1W ' \ __ .L. h m 1 ("a '; \ + 2W —' ‘4 k 4 7 3;) 49! 04 O (3 pts} (b) Find the 10th derivative of ﬂat ) * eT —/2€6/+§z2+)0 ,.»-—" i We) : eff i (3 pts) ((3) A particle has position (or displacement) given by 5(t) = t2 7 61: + 11, Where t is in seconds. At what instant does the particle have a velocity of zero? SCOL’Clubt +-\\ s’GO=v-— Zt-lo 3 O: 2t*lo Q2 3 2t JC 1 3 '1' r H»; 5. Let y x 51:4 — 4:33 2 m3(x — 4). The ﬁrst and second derivatives are 3," 2 42:3 w12332 = 4332(2: — 3), and y”212:c2 — 24a: : 12\$(sc r 2). {2 pts) (a) What are the :r—coordinates of all the critical points of the function? \5': a”?— (x45) 0 = ‘lxz o N... X (3 pts) (b) For What values of 3: is the curve increasing? For what values of :13 is the curve decreasing? '2— a 03 l : 4V (IS—‘73) b) (—0 z 4002" L4“ :3) V '- 4 (A) 1 "" Us A of} ___.._ -» — ~- ~ +++ [5'03 ”' 4L01(\'®= 9?: X q '00) ~— 4100)" (lo-'3} Wan "100 ' #l " (2 pts) (c) At each local maximum or minimum point, state whether it is a local maximum or Ininiinun1_,_____ and State its; (33d 13319314) ( was" a locdl 'm\mh\(iih gL’D 7. 11(4) = -17 qum “YEW 3 WWW... __ __ _ O, ,. v3 \3 mcr‘eOtthWJFzSFWC%#§D decrEQSmci tor (-00. ’5 ‘V CL (3 pts) ((1) For what values of m is the curve concave up and for What values of a: is it concave down? Lj H ____ \ZX (Xvi) Lj "(\) -_ \2L\)(\-Z) ; ”ll o 2 max ~73 (,3 "(—0 : lat—Devwao 3 o 1 0.x 0 : x "7— g ”(m : ammo-2): + K; x=2 w ,, maeup Arm—Jr ~ ~ —~- HM W on was?) 0 and comm down on UN 2 .--—«~—-—h_.__, ...
View Full Document

• Fall '00
• staff

{[ 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