Math 2A S99 Midterm

Math 2A S99 Midterm - Midterm 2A, 2/5/99 Name 1/ ...... __...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

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

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

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

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

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

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Midterm 2A, 2/5/99 Name 1/ ...... __ ID# .......................................... .. 27/29 1. Find the equation of the line passing through (1,2) perpendicular to 2y—4a: = 9. (3pt.) @ éy—‘a/X: y-a'i: -//g (x-/) éerXf? yr2:_//&x+//& y: anfq/a w @ 2. (a) limit—>0 Sijigiiimzx =? (2 1’“) (b) 11mm1 I“-1 =? (2 pt.) 2—1 m 3X -LW W3X MEX _ ' ‘ e 1 3x I E (02%;; _ “a ‘1 £1» m.¢f _? E WX'JLI/n 0'9! Max Max )HD 5x gun/K gum x % ”« Q kayo 3x X?c K X” """—" — / ~— 7/“ 4"“ Al”- 2. MM x‘h/ ; Jam (“00‘”) _. LA; (MIN/x4000“): 1 X9! X..l ya/ [X_f) X3," WI) x04" (“i/XXI“) =13»? X5+X2+2<+l =(:)3+n)’+r+;=m X—H ya] “"" (W _ #4». W1 (2.. fiiWflmuM 3 LI X - 2 @ 3. Show that 1'3 + :1: +1 = 0 admits a solution in [—1,0]. (5 pt.) J‘W'q W) m a cambww Wet—Hr“ fan“. (4- I; G ) (PH w d [_$ 0:] é / may) 041 WWcht-J MWt; m 144% a ;W C 0“” [‘50:] WCA :0 C. 4- (a) (f: — 3% =? (3 1313-) “’J (b)flat):(x2+(2$+1)2)3;f’(w)=? (3pm 0 i - i5 = x" —LI><2+V>< , >6”-L}x2+4x 1: ()(x" )3 ((x‘MX-J) guy; ) : (fljx"+"x) ’ “if:82;£5.1-i>:?+4><)z><3:z 0' ’ CX”')<’)2 (1‘ : {ng—8x+4)(M)/:<4—9x1+#x)(wa—axl) :fX/XUI ' 12) W) = 5(x1+(2x+l)2)1' (xzmthfi): ‘ V? Z ‘ (01X + a? (wax) . a)? (ISXZf/oIX+3)Z’{ch1’—8x +9) .: /_— 3(jx2+.yx+/)2. (/Ox+l;37/’ 3 X 5. Find the maximum of 9(1') 2 3; + i 0n[%14]. ‘ 90): QXZH I)(x: 2’ 02% )3 (5 pt.) #xKZx) “{2x2+1)C2) 1 “W (2X) (2x)2 a?) Crfl'Ica' Pomfi L/x La? _ 0 HT- (2X?z 9X1 “772 ' x: J1; / 3 Exlrrema ) Lf/vA; / (i a r “W q) / LII) (i0)73ioo +1 : E+§ D (g : 33+; _§§_ j ’ 3(l/lo) J 2/” :%' ) 3 - 8 T1— : r .1 i 5 (V2) :{ 3 : W Max " ) 6. The sum oftwo nonfiegative real numbe bis 10. What is the maximum oftheir product? __ - 6 t. 69/ Q+b-IO waml h) (P) / b:lo_q maxlm12€ 01b - i q 097“? _ v? :00 w [j o) w’J ') y” Io-aq 2) lo-mo - AG IO 5“: CFH’ICCH aé'rfi' 3) EX+Y+=W1Q I. O) )C) j I “J, I) L/’- Midterm 2A, 3/1/99 A‘ s 1" (Psu'uz 1. Differentiate the following functions (a) me) = (b) g(:r) = esin :32. a) WOO-'5” X (“2 “£5” 9‘ [’3 - (1&0 x 7 x, x z - .. A) j ’0‘): /‘.£A?n)cz 1' X (aimx;m-‘3x) 2. Determine the slope of the tangent of the curve given by $15 + J—z + 2.231 = 4 at the point C V2) -1) Final 2A, 3/19/99 Andras I. Stipsicz 1. (a)li1’ng,_*_1£35-ji)3 =? r2—1 (b) : 351:2 +cosw. Determine a) ADM (“00:41”) i x“ : -/4.f : )6-‘"" (finfixd) X-v-I Xv! '52 J‘Uéj/rf-vli gap m1 4’ ‘ )1 : O [Limit-,0“ 1.; {‘msfrrwaf c m“ X % -} . ‘ 4 (fix) 73x 2+ caret 1W0) X} ‘3. Show that the equation 1'4 -— 73 +5 I 0 has solution between a: z —1 and 3: = 1. 7X} ’lcbbhcl’tfin L}- GfiIT'Ufl-wuum (AMW C4 a 7&017’;ne'wfd ) 0’?‘ {A} [—/) I] Md MALL PF”: (5,)”- 7m)+5’=/5 ._,_ 4 __ _ FC/):(U4 —7(r)+6’_-‘“l f“) I 04/3 f“) 7/40/Lmb/ou/ A; w wmmwm (ml/w jute/#13, Wu Mth NW c W 1250 mm.» Haj-:0 3. Differentiate the following functions. a) = (ch + (30554:)2 b) g(x)=—l—+4 {mm UH +‘7’ sinr 0) 1f ’(x) = 6;" (xszox)- (xz+mx)’ : 2(x2+omx)' (9x w». X) Wu) : JCXZiFQO/Jx) (Jx—JZJQ-rx) 4. Evaluate the following integrals a) In3 sin :1: cos Idl‘ b) fjl(%+x8)dx f -\V x J I ,2 .7 W4 '1 I” I 7;; j -/ "" A}. ' In “ __ F _ ‘t fli- 1 Hr L ,2 a): 4'3,“ z ii?) [93 MYI?X]0 [92 5. Find the maximum value attained by the function f(:l¢) = x3 -— 3x + 10 on [—2,2]. :) 1£)(x):3x2'3 2) am «ma w m. Ems“ Everj""uhfirc frlhcai P’}S h": 3) EX‘HC’MQ T -2/~;) I) 2 a“) {(-2} -8+(DHO‘8 _~— 4" {—1) —j +34IDHI-Tg HUOUW‘U’“ Ll/Dq—‘l {L J' I—3+[of o ‘6 IL) 8-(O+’OZ‘ 61 r_._,___—— V A: Xj % X72_‘Iq2:ibz X1+Lj2:0?5(, j J j’zrgm-W klfjflij’“ J 7. Find the critical points and inflection points of the function = 31:31 — 7m. yel- O 7><"’?:7 W54 xiii / i (r-[Jrlfai = i "i ,| Max */ \;Mlh / \) 4W“): 7x“) -7 8. Sketch the graph of the function m) = 31%— 7x. K;_l__u_l‘f_‘ i't“ rig/1' f a; “14;” M P i}. S I) 1‘ ’ J $0»:- (0) 3—750) Krijx-; fl I = O I 1 ,— iw) {(K] Ina} im¥iCCilvn V1? at X-0 y m+€r(PP+ 0+ 0 X: ‘i is a Maxlniunt 5 11. Solve the initial value problem f’($) = 41' + 3cossc and f(0) = 4, 4r(x> H2 X1 "l" 3t,.'!‘113“- + C 12. Evaluate the following indefinite integrals a) f(sin 1? + 4)dw b) fix? —- fl + 3$)d1‘ ...
View Full Document

Page1 / 13

Math 2A S99 Midterm - Midterm 2A, 2/5/99 Name 1/ ...... __...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online