Math 2A S99 Midterm

# Math 2A S99 Midterm - Midterm 2A Name 1 ID 27/29 1 Find the...

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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‘ ...
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Math 2A S99 Midterm - Midterm 2A Name 1 ID 27/29 1 Find the...

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