test2solution - WTIQN/Mé‘rflmatq me Name &...

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Unformatted text preview: WTIQN/Mé‘rflmatq me Name & student no.(print clearly) MATHIOI3C 3.0 Test no. 2 F2009 Time: 45 minutes Value: 100 marks No graphing calculators or written material allowed. (Marks) (25) Q1. Consider the function y = 2 - 2x — x2 . (16) :1) Obtain y’. (£6) b) Find the equation of the tangent to this curve at x:l. '3 : mow _ '/z. ‘1‘: O_ éC2,xr><.) -(2‘ly‘) : 16—! N‘DKW‘: film“) l'K—L’” of L2! k1: 2"JZI-«1L= I ...to he continued... , (25) Q2. d 1 (l5) :1) Beginning with the definition of a derivative 115 a limit. prove that—d'fflx”): 6x. ‘ I I d 3 lim bla-bla LC. begin With max )=bla_,b[a bla , Another other method will be given little merit. v \r‘” (10) b) If C and B are constants, evaluate lim siniCx} w x—ao cant—Bx! J ‘3“) / up”) W ch z/Qr'v-e Siw‘flcx MKBV x44: CV E; (N... Slant-x. LL. 9;,u57‘ pact ox sin-$1 5" .._tul\c continued... , j...» s'mcx 1,3... ’x—aa ET'F-eaug‘ 5"" I I. .C.’ :W ___._._-—- B I ‘5 w (25) (‘8') (8) (9) Q3. Obtain f’(x) and simplify as far as possible if: a) f(.r) = cos3(tan 2x) 1' b) f(.r)=|n( ) lx+li c) f(.r)=“y+a_x whereaisapositive constant (i *(I 2. Wm - senlCfimlx») ‘WCWZQ 5’“ 7‘" —_ _ Maui’me MCWZ") ‘3‘“ (twang | : W4 2 ‘ W i Wm M "I l 01 X : ‘ m: arm 72:.) 7%“): :5?» or“ '“o W” kw“? - 2 «.3; : ( @WK‘C‘H) 34:.(14-1) wow”) I I -. _i__,f “ 7. * ;:. new) W MW _ ' -1, I)“ C) '9‘) = Lax-a“_)(c£¢.ofx)lwo~ ~(&K+a Mafia ) Q ;_ ....... ._.,r . 77 awn—nimww ‘7 I g (0‘1 ’ 0(1) ugljlmgwh, f” . Li w UK, ‘1): M 1 an). M - W“ Max 0» -29.,«9; +0. )—(a +29% Azimw'b‘j’ WFW’ 13w“ '- i rd?“ 1 ?WW (9:2 or)" — Zia/£31, w Him I Laird—x) '- --l”hL‘L‘HINiHLIL‘d.._ (25) Q4. (15) a) Let 2x2+y2=6. At x=l there are two values of y. Identify the two (x,y) pairs that satisfy the above equation. Corresponding to each of these locations, evaluate dy/dx. (You may use implicit differentiation if you wish, or any other valid method.) (10) b) Find the exact values (i.e. not approximate numerical values) of the absolute maximum and minimum of the function y(x)=xe 3, Osxsl_ .. “,[f M OIFmewi “TAM fr _ Wk “1 “Mme” 3": if? ...to be continued... V‘IrrO W 2 “wk/“fl ’ Ir; (—d+( —% 73(- I a ' i ) “(6 May) “*meifi d e‘%< l_ :0 wefim J ‘1 ‘ Awaw ENDOFTEST ...
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test2solution - WTIQN/Mé‘rflmatq me Name &amp;amp;...

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