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Ernst_Test_1_Spring_2007

# Ernst_Test_1_Spring_2007 - MATH 101 Test#1 ‘5 NAME Ms...

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Unformatted text preview: MATH 101 - Test #1 ._ ‘5? NAME: Ms. Ernst <3 2— " APRIL 27, 2007 7 1. (10 pts.) Find the vertical asymptote(s), X-intercept, -intero_ept_, and the 9f}? horizontal asymptote. Sketch the graEh. (é ,L Hrs? j E}. _ 2x + 3 + E f(x)=x_1 - l fﬂﬂ , j 1,: ’5 _ F: -— -- —' __.. f ' F 7— I ‘ \ —-~ ._._ ""--~.. A} \mr‘l’ f3:r._'..,2wp§o1’- 3. X3} .--_ \ 'r .L-A-“Vm‘i'ﬂ-iﬂv—k 5,. r 1-?” IrIJ' %}n,f.¢: ' ‘ I — I I :4} f r '/v! ﬂavibreg Y’ I’M-22'- Y:1#E'l~:;lbh ...}— Cr)kllL.I-*£WP¥J4{I' -: "z ~1J/L GA, “wquﬁr E .H. "I' 'kpq r." : tar .‘ :— H __i k w n W 3 ,ﬁ a: 0:.“ drrguo-Mihnfﬂr '-— O 0'" X—\ ’ j i; if 2+ % Q '9 MW“ 0 2x 13:0 x(1— 3?) . i533: w 5’" : "3 :" ”'"Fh'"; T: _.r_'l-J I — k t ' ‘ i) " c 11 2. (6 pts.) Use the deﬁnition of continuity at a point to determine if }'(x‘_) 'is continuous at x = —l. 2— if, 'I. .- ' x2 1: xi—l -.._..__[2:.' 5...!- '«' f ‘- x +x KW“; K ﬁx): 3, x=—1 3 (3“ \5 r; E I r I {\0 rm “,7" .1 1 .- t i ,4/-| A"? a. lim f(x)= [ f. my {(x) = i x—b-dn 1..» ' 13- x131}; f(X)=—-C>c: g. 31% f(x)=*j_ c. 133 f(x) = + be h. 111%. 130:) = (int d. x1531}: f(_x) = cine i. f(_2) = 3 e' 5‘3 ﬁx) = 1 j- f(0)= 55%: .6, (8 pts) Find f '(x) using the limit deﬁnition of the derivative. f(X)=2x2—5x+1 gléqwz qK-FS' h"?0 ‘n . q M b/‘Hi‘ ”i Lin-"Sin. / / Q “1 - 5‘4 \/L{k+lirt“5> i ‘ {ﬁlm—Pix} , Sﬁx+laj+i>x 1" B U li_ {m — ._.— _'_ k guy-ril-ﬁu k [3* "5k 4-0“ 1?? Vin ~| /« “kin flint %—%kK—}({r+%7’f ' (Hit-Li'linl-Sig/L ._.._/J 5. (50 pts.) Evaluate the limits- if possible. Draw the graph when necessary. Explain a. your conclusions. lim __.._"2+x‘2 Mix fl) :x"—-)l '2 _1 --‘ ' 1 _l E ”LAW .- 2+1: 2 “,— "‘ “f” (Hal-1) ”A lim 2:2 +38x—2O (k-H'D k *1) x—9 "2' ‘- ’1 lim 2 r '«.__ x—>—’8* x+8 "Er-h - '§—"""?“TJ£ "'*' :15... 9 4! lim 3‘3 (’33 ’5’"; x—r _ _.--"""' ‘ K 9 x 9 v3 [g6"w(\‘:“3) . 12x3 +120 :1 (a 111.2 .-4 '3 L31 x-> x. +x x3(’~+ .I) z; 11+ D E 3,3 x. + ‘I x .‘irl-l ﬂ :{3 f? :37 :44 f 1 1‘ 7 V, . 119:9. :31— 71“ I" if I“; q+lh W‘ik ”wig " _________....~-—-—-- 5 11"“ Ll" I (Q‘hlélr'h (w ,, ,‘K '2 N v 1 q} 5/ f I q-FF' ”(M3 % (2+ I 91-11%. (111.0) C? ' *_.rr--;'—”" __ _, f/O Mu“) g s a, {,2 9 "I. 1 _/" -511; gt" -1 1:»! 1.. a 1 31. was If £50 n+9 if“; 7:? ”F— '— J 5 ‘ S ( 3 F53 Z V L9/< llm : i 5 you) (gl 5, h'ﬁ Lear 0.6;: In Bahamian?“ 4 r:|£.— g. lim tan x x—nn'Z" 4/ L: . 7x "-le ...,\ _ g)‘ * ,7 h- 31?: 1—77 ’ eff _, ,1._-I~( [{K 417‘ f 9/ ,, ‘3 9 5 ‘2 / _ 5 7. ('6 pts) Find the average velocity of a projectile on tlie time interval, [0,1] secbnds if the height of the projectile is given by, .-; s(f)=64(—32r2 (ﬂ) B“: if. _’ ’5 li‘C-“ﬂ‘ﬂ WE): (”H-(”w .uaV' 15/“ £49 CWT Wt.” ‘f ,_, gym-C»; - a 1:51,: _ [my—(qr, 5 W- -C::f:/ :M 9-9:: we: ...
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