Sol-165E2-F2002

Sol-165E2-F2002 - MA 165 EXAM 2 ‘ Fall 2002 Page 1/4...

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Unformatted text preview: MA 165 EXAM 2 ‘ Fall 2002 Page 1/4 STUDENT ID I RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. Write your name, student ID number, recitation instructor’s name and recitation time in the space provided. above. Also write your name at the top of pages 2, 3 and 4. 2. The test has four (4) pages, including this one. . Write your answers in the boxes provided. 4. You must show sufﬁcient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes or calculators may be used on this exam. 0»: (16) 1. Find the derivatives of the following functions. It is not necessary to simplify. ' I = 3 3 —— ‘ ’3 5/5 C Maui '1 V 1‘ {vii “WSW (a)?! v1+\$ _,.(1+)() VNF- LDng f )L {in A, 3 -?"”" 2 am Aux-av in siivkliid‘gzmé; EM ': %<1+X) 33X , . oUY. . ’ “R r ' (b) fa) ; tan”1(cos2 x) g/(x) : ~2sinstx .1 + C0541 MA 165 EXAM 2 Fall 2002 Page 2/4 Name: (8) 2. Find all points (33,31), with 0 g :c 3 2w, on the graph of the function f = 2 sinw + sin2 96 at which the tangent line is horizontal. «it intras- mLoiAAﬁf-Me} Mcij ;~ , Eg/(x): 2mm! +2siwy¢osx v aft ' @ g/(x):‘0 2 2msx(1+\$lnx)=0 ® 1‘ “TV SIT mJX=O ”" X -?).—i—w 8.31% :4. ax:‘§é§ x-T-g 4g32+i=32 x:%”‘.,~a:~‘2+l:'¢ (9) 3. If y = 2:2 + 1, ﬁnd d—y by implicit differentiation. x~y dx (“‘09 6‘? "Mi'dﬁﬁ : 2.x @ (m; (x—S) 5% .— ~é+ %% 32X (“JD—)1 x.%¢ ‘3 “(X-'1)??? (9) 4. Evaluate each expression: (a) sin”1 7:: ‘2 43-? slnj:' a: NFC - —1 f4. : 0:3 ‘1 (c) 5111 (cos 5) \a S g (‘3 5 Sin? zril-mslké' :: \lidéf‘; 1"":- hem \$95 511' (6) 5. Find the second derivative of the function y = M 1 3 7. ._-———‘: >< ‘rrxa (9—) d1 7.. I 2, 7 s _ MA 165 EXAM 2 Fall 2002 Page 3/4 Name: (10) 6. Find the derivative of the function y = 321/? " V «3—;xi/x ': QQMX x: ﬁlfTme @ die. 2%” “30.” «k 0 If: X ._ 1-3m: i/x 11.. __ e ___{._ z x a“? X x (14) 7. A kite 100 ft above the ground moves horizchltally at a speed of 8 ft/sec. At What rate is the angle between the string and the horizontal decreasing when 200 ft of string have been let out? 0U: :00 air" 50 iojzwkvovn t .31 ' ah! 'w (6) 8. Find the differential of y = 111 v 1 + :32. 4 bra—2de n» ” -— 1 . A 1x \ﬂ'fC? 2‘ “X " R MA 165 EXAM 2 Fall 2002 Page. 4/4 ‘ Name: (12) 9. The volume of a melting cube of ice is decreasing at a rate of 10 cm3 / min. How fast is the surface area of the ice cube decreasing When the length of an edge is 30 cm? d}? PM: a}; dim M300“ ~ 626%- ,, g3; gyms? vsxae OLS s: eve/3(3) :igxéléj at wax/(ﬂan our EU: ‘ ' ‘ 5E :65” BE“ x M We. mud- to {ifhck‘djﬁg‘ﬁ-M'xw’ﬁ‘of" ,“ran: (9 a .. ._.. \l “:— x 9 _. “run/t fox, we}, mihov nucmuiml an“)? (10) 10. (a) Find the linearization L(a:) 0f the function f 2 (3—23 at a z 0. L(x) f.— 1510.7 + g’m (ML) ® Em: c’?” f’tw)=r2e"“ H0) = i Wok—2 L60 : :L —» 2 X (b) Use a linear approximation to. estimate the number 6“”. ﬂ . ,_x i“) ~93» LU) {AW x nm'r 0.. 95- e ‘25 1-K #VXMA-rﬂ CFOIZN a ;/0.93:n '8 ...
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Sol-165E2-F2002 - MA 165 EXAM 2 ‘ Fall 2002 Page 1/4...

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