exam3sol 17A - Math 17A (Fall 2010) Kouba Exam 3 Please...

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Unformatted text preview: Math 17A (Fall 2010) Kouba Exam 3 Please PRINT your name here : _______________________________________________________ --__ Your Exam ID Number __________ _- 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. . 2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT’S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION. 3. No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM. 4. Read directions to each problem carefully.‘ Show all work for full credit. In most cases, a correct answer with no supporting Work will receive LITTLE or N 0 credit. What you write down and how you write it are the most important means of your getting a_ good score on this exam. N eatness and organization are also important. 5. Make sure that you have 7 pages, including the cover page. 6. Put units on answers where units are appropriate. 7. You will be graded on proper use of derivative notation. 8. You have until 9:50 a.m. sharp to finish the exam. 1,) (6 pts; each) Differentiate each of the following functions. DO NOT SIMPLIFY ANSWERS. D l l a.) y=111(a;2+2’3) --? y : z x' (XXLR‘XfiYI 2) X 4—2 I D b.) f(a:)=e2"”cos(e’) '—’I . X XX ~9'Lx/z ea". ~MCeX)-e, 4— Ac . w (6‘) c.>r<z>=@mr —+ fin fix) = M (ij x= x-MMx) 1—)» 4— -~9'é<): x32!— Mx+mfiné4mxj ——> flw x +bq:@m%fi[§%§anahxfl _Hfi fianx 4e¢x X 2 \ e m X M X / Xx Mx W :1 2.) (7 pts.) Determihe the x—values for which the function f 2 I2: 4 is increasing (T) and decreasing (1), DO N OT GRAPH THE FUNCTION. 1% +7.. 5? \— l E 1. -t (b. I X r\ X) X l I t I X p .. 084%); ((144,); _0 fl q-Xlzo —-» X: /*Q. ~ 0 4— O -—— 1 _\~_ X:_Q x:.1 3‘) (12 pts.) For the following function f determine all absolute and relative maximum and minimum values, inflection points, and x— and y-intercepts. State clearly the x—values for which f is increasing (T), decreasing (1), concave up (U), and concave down Neatly sketch the graph of f. f(a:) = a:(a: — 4)3 on the interval [—1, 5] l L 4-0): x. 3(xaqfl4— l» LX- 4!) 3‘ -:. CX—q)°.* [3X—L (_x~q)] : LX—‘lf‘ [4x— 4] = O ?/ _ o -+ 0 +- W 4;! Xz-l x=l >§=q KW” Y: (.15 ‘f=‘aZ7 =° “E5: ’vv-d W REL. ABS. ABS. MAX MAX. MIN‘ ' ' ——» 41%;) z (x— ~2‘@)+ 2 0M) PW ‘I Y 7/ 4, o "" O 4— 4:” Ks‘l K201 X34 x357, Y:-IL Y=O INFL. we. INFL. (we. Vic 1554'? I<x<qjq<x<63 Yieo \L W -(<x<l/ 'Yg UM ~I<X<2/ q<x<5’/ YMA 4m a<x<q J- 4.) (7pts.) Cesium-137 is an isotope produced by nuclear fission, and is used in medical radiation therapy devices for treating cancer. It’s half-life is 30.17 years. If a sample of Cs- 137 has an initial mass of 100 mg, how much will remain after 250 years ? Nzccké Nzloogwflfl—ap Q:loo‘, ) 4: _ ‘_ ._ N : (DOCK )‘t—30J7 M N— "—3 6.0_loo €3OJ'TK a L __ €3Qi7k A - a __ .l'7 140/1 MO/RjZ/Q’fle30 k: 30.l7K—-» k: MU/ N- (00 C 30-(7 ‘6' 5.) (7 pts.) Consider the function f (2:) = lnrc defined On the closed interval [1, e], Verify that f satisfies the assumptions of the Mean Value Theorem (MVT) and find all values of c guaranteed by the MVT. +LX):,Q44X CM a)? [(16] M ‘P‘OQ: 31(— 4» law cm 0/6,)3 26M 1;? MVTMRWM m #07 I<Q<€,)W I _. 484410 4C0“) 717—): e-: “e—z e~l ' 6.) (7pm.) The function f(m) = a: + x3 is one-to-one and has an inverse function y _—.= f”1(m). If f(2) = 10, then what is the value of Df‘1(10)? 4‘3}: H 376 M 3) fax} : | _‘ —=,, 4 Gt 0‘2} —i | i i ‘0 : ~ 1 i : ‘ D“?— C) gJ‘LJ 4"1062/ I 7.) (7 pts.) Use ailinearlization to estimate the value 05 (8.5)1/3. _ ‘3’ ‘ Mri—Qc): x/3 M a: 5’ —->J;-'LX): ELK 3:3’FV3-J L(x)=-PCA)+~F'C«)Cx-«): 4432+ 43(3) 093).» . I i _.I__. LLx): 8/3 +3C?)% CX—J’): gut-5&6!) LX—X‘j —7 LLx/z (1+ Tia-(x47) j W I (8.67/32: LL85) 2 2+ [45(3515’22 «1+,{zéé/ I "' (KW/3 1 21- ~ 3 0417 8.) (7 pts.) The edge a: of a cube is measured with an absolute percentage error of at I most 7 percent. Use a differential to estimate the maximum absolute percentage error in computing the cube’s surface area. . lAXl ‘ L “477‘, ‘ n - $-6X I W X e. / k M Legit L451” 145] x ( S S 'V S \5.A><l (tax/ix! _ ;(A>(l : —————~: éx ~02 X £02<767°/ v». 9.) (7 pts.) .A closed rectangular box with a square base is to be made from 54 02.2 of umterial. What dimensions will result in the box of largest possible volume ? Y MRXa-é—‘(XYz 54/ ———» _ _ 3A . 10.) (7 pts.) The Bedbug Motel fills 100 rooms if the charge per room is $40, for a daily revenue of (100)(40) = $4000. For each $5 increase in price, 4 fewer rooms are filled. Use - calculus to determine what charge per room will maximize revenue. insexwtarrs' 4"; _/ 294v»? W I4 = crmth rpm) —=’ 14 '4 (904-50000qu Q, (2 qu+€x](;q/+ (5](Ioo-qx/ :— ‘léo "' QOKwLé'OO -'ROK : 340.. qox:o ~—9 x:3iE/:Xl{ #57V5 «2’ + 0 “- l W X2676 (VIM/7.3. '. QO+CK57<57 : #80150 :Hsfbo-W'. I00» qu.6‘]: 66 W M. K: #5445 ,2 1 1 l.) (4 pts. each) Consider the function f (3;) = L + gv—l ' , a.) Use limits to find equations for all vertical asymptotes for/ f. M xl+ I : 3‘" : i 00 M’ ><*a I ><~ I O V A . AA X = l X+ ! I b.) Find all tilted asympgojes for f. x.- l —«“—LX):X+( 4- WM ~(XLX/ x+1 ' _ ~CX~(') (j_x+[! L- The following EXTRA CREDIT PROBLEM is, worth 10 points. This problem is OP- TIONAL. - 2=+3¢ 2=+4z' l . X X —— . LX l X M Rx+3x . 7’" — M (a 4(4) XQ‘LW 9~+q 7:2 A—o 1.) Determine all horizontal asymptotes for y = - X x I. _ X" 0°2+H 332 X400 ‘+(&)7< _ MI l+ §—*x a l+o :1 X-fir—oo {+C_I£‘K ‘ l‘l-O ...
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This note was uploaded on 11/26/2010 for the course MAT 017A 69453 taught by Professor Craigbenham during the Winter '10 term at UC Davis.

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exam3sol 17A - Math 17A (Fall 2010) Kouba Exam 3 Please...

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